内藤 敏機
| 名誉教授・その他関係者 | 名誉教授 |
- プロフィール:
1969-1985 有限次元空間での無限の遅れをもつ関数微分方程式の基礎研究
1986-1998 無限次元空間での無限の遅れをもつ関数微分方程式の基礎研究
1999-2002 関数微分方程式の作用素解析的研究
2003-2005 差分方程式手法を用いた微分方程式の研究
研究者情報
研究活動情報
論文
- Periodic solutions of difference equations
Tetsuo Furumochi; Toshiki Naito
Nonlinear Analysis, Theory, Methods & Applications, 71巻, 12号, 掲載ページ 2217-2222, 出版日 2009年12月, 査読付
研究論文（学術雑誌）, 英語 - Delayed Feedback 方程式とその性質
宮崎倫子; 内藤敏機; 申正善
RIMS Kokyuroku 1637, 数理解析研究所講究録 1637, 1637巻, 掲載ページ 74-86, 出版日 2009年04月
研究論文（大学，研究機関等紀要）, 日本語 - Stability and robust stability of positive linear Volterra difference equations
Pham Huu Anh Ngoc; Toshiki Naito; Jong Son Shin; Satoru Murakami
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, JOHN WILEY & SONS LTD, 19巻, 5号, 掲載ページ 552-568, 出版日 2009年03月, 査読付, We first introduce a class of positive linear Volterra difference equations. Then, we offer explicit criteria for uniform asymptotic stability of positive equations. Furthermore, we get a new Perron-Frobenius theorem for positive linear Volterra difference equations. Finally, we study robust stability of positive equations under structured perturbations and affine perturbations. Two explicit stability bounds with respect to these perturbations are given. Copyright (c) 2008 John Wiley & Sons, Ltd.
研究論文（学術雑誌）, 英語 - Lyapunov exponents of solutions to linear differential equations with periodic forcing functions
Toshiki Naito; Pham Huu Anh Ngoc; Jong Son Shin
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ACADEMIC PRESS INC ELSEVIER SCIENCE, 342巻, 1号, 掲載ページ 349-353, 出版日 2008年06月, 査読付, We give Lyapunov exponents of solutions to linear differential equations of the form x' = Ax + f (t), where A is a complex matrix and f (t) is a tau-periodic continuous function. Notice that f (t) is not "small" as t -> infinity. The proof is essentially based on a representation [J. Kato, T. Naito, J.S. Shin, A characterization of solutions in linear differential equations with periodic forcing functions, J. Difference Equ. Appl. 11 (2005) 1-19] of solutions to the above equation. (C) 2008 Elsevier Inc. All rights reserved.
研究論文（学術雑誌）, 英語 - Representations and asymptotic behavior of solutions to periodic linear difference equations
Toshiki Naito; Pharn Hun Anh Ngoc; Jong Son Shin
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, KOBE UNIV, DEPT MATHEMATICS, 51巻, 1号, 掲載ページ 55-80, 出版日 2008年04月, 査読付, We give a new representation of solutions of the periodic linear difference equation of the form x(n + 1) = Bx(n) + b(n), where B is a complex p x p matrix and b(n) is an element of C-p satisfies the condition b(n) = b(n + rho), rho is an element of N, rho >= 2. If B = e(tau A), tau > 0, then the equation has two representations of solutions based on A and B. In particular, the representation of solutions based on A is deduced from the one based on B by using the translation formulae from B to A. Using these representations, we can obtain the complete classification of the set of initial values according to the behavior of solutions. As applications of these results, by the initial values we characterize necessary and sufficient conditions on the existence of a bounded solution and a rho-periodic solution.
研究論文（学術雑誌）, 英語 - Floquet representations and asymptotic behavior of solutions to periodic linear difference equations
Toshiki Naito; Pham Huu Anh Ngoc; Jong Son Shin
HIROSHIMA MATHEMATICAL JOURNAL, HIROSHIMA UNIV, GRAD SCH SCI, 38巻, 1号, 掲載ページ 135-154, 出版日 2008年03月, We give new representations of solutions for the periodic linear difference equation of the type x(n + 1) = B(c)x(n) + b(n), where complex nonsingular matrices B(n) and vectors b(n) are rho-periodic. These are based on the Floquet multipliers and the Floquet exponents, respectively. By using these representations, asymptotic behavior of solutions is characterized by initial values. In particular, we can characterize necessary and sufficient conditions that the equation has a bounded solution (or a rho-periodic solution), and the Massera type theorem by initial values.
研究論文（学術雑誌）, 英語 - On stability and robust stability of positive linear Volterra equations
Pham Huu Anh Ngoc; Toshiki Naito; Jong Son Shin; Satoru Murakami
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, SIAM PUBLICATIONS, 47巻, 2号, 掲載ページ 975-996, 出版日 2008年, 査読付, We first introduce the notion of positive linear Volterra integro differential equations. Then we give some characterizations of these positive equations. An explicit criterion and a Perron-Frobenius-type theorem for positive linear Volterra integro differential equations are given. Then we offer a new criterion for uniformly asymptotic stability of positive equations. Finally, we study stability radii of positive linear Volterra integro differential equations. It is proved that complex, real, and positive stability radii of positive linear Volterra equations under structured perturbations ( or a. ne perturbations) coincide and can be computed by explicit formulae. To the best of our knowledge, most of the results of this paper are new.
研究論文（学術雑誌）, 英語 - Translation formulae and its applications
内藤敏機; 申正善
数理解析研究所講究録, 1582号, 掲載ページ 108-117, 出版日 2007年11月
研究論文（大学，研究機関等紀要）, 英語 - On stability of a class of positive linear functional difference equations
Pham Huu Anh Ngoc; Toshiki Naito; Jong Son Shin
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, SPRINGER LONDON LTD, 19巻, 4号, 掲載ページ 361-382, 出版日 2007年11月, 査読付, We first give a sufficient condition for positivity of the solution semigroup of linear functional difference equations. Then, we obtain a Perron-Frobenius theorem for positive linear functional difference equations. Next, we offer a new explicit criterion for exponential stability of a wide class of positive equations. Finally, we study stability radii of positive linear functional difference equations. It is proved that complex, real and positive stability radius of positive equations under structured perturbations (or affine perturbations) coincide and can be computed by explicit formulae.
研究論文（学術雑誌）, 英語 - Characterizations of positive linear Volterra integro-differential systems
Toshiki Naito; Satoru Murakami; Jong Son Shin; Pham Huu Anh Ngoc
INTEGRAL EQUATIONS AND OPERATOR THEORY, BIRKHAUSER VERLAG AG, 58巻, 2号, 掲載ページ 255-272, 出版日 2007年06月, 査読付, We first give a criterion for positivity of the solution semigroup of linear Volterra integro-differential systems. Then, we offer some explicit conditions under which the solution of a positive linear Volterra system is exponentially stable or (robustly) lies in L-2 [0, +infinity).
研究論文（学術雑誌）, 英語 - A representation of solutions for periodic linear difference equations
内藤敏機; 申正善
数理解析研究所講究録, 1547号, 掲載ページ 59-67, 出版日 2007年04月
研究論文（大学，研究機関等紀要）, 英語 - Stability radius of linear parameter-varying systems and applications
Pham Huu Anh Ngoc; Toshiki Naito
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ACADEMIC PRESS INC ELSEVIER SCIENCE, 328巻, 1号, 掲載ページ 170-191, 出版日 2007年04月, 査読付, In this paper, we present a unifying approach to the problems of computing of stability radii of positive linear systems. First, we study stability radii of linear time-invariant parameter-varying differential systems. A formula for the complex stability radius under multi perturbations is given. Then, under hypotheses of positivity of the system matrices, we prove that the complex, real and positive stability radii of the system under multi perturbations (or affine perturbations) coincide and they are computed via simple formulae. As applications, we consider problems of computing of (strong) stability radii of linear time-invariant time-delay differential systems and computing of stability radii of positive linear functional differential equations under multi perturbations and affine perturbations. We show that for a class of positive linear time-delay differential systems, the stability radii of the system under multi perturbations (or affine perturbations) are equal to the strong stability radii. Next, we prove that the stability radii of a positive linear functional differential equation under multi perturbations (or affine perturbations) are equal to those of the associated linear time-invariant parameter-varying differential system. In particular, we get back some explicit formulas for these stability radii which are given recently in [P.H.A. Ngoc, Strong stability radii of positive linear time-delay systems, Internat. J. Robust Nonlinear Control 15 (2005) 459-472; P.H.A. Ngoc, N.K. Son, Stability radii of positive linear functional differential equations under multi perturbations, SIAM J. Control Optim. 43 (2005) 2278-2295]. Finally, we give two examples to illustrate the obtained results. (c) 2006 Elsevier Inc. All rights reserved.
研究論文（学術雑誌）, 英語 - Characterizations of positive linear functional differential equations
Pham Huu Anh Ngoc; Toshiki Naito; Jong Son Shin
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, KOBE UNIV, DEPT MATHEMATICS, 50巻, 1号, 掲載ページ 1-17, 出版日 2007年04月, 査読付, In this paper, we first prove that if a linear neutral functional differential equation is positive then it must degrade into a linear functional differential equation of retarded type. Then, we give some explicit criteria for positive linear functional differential equations. Consequently, we obtain a novel criterion for exponential stability of positive linear functional differential equations.
研究論文（学術雑誌）, 英語 - Stability radii of higher order linear difference systems under multi-perturbations
Pham Huu Anh Ngoc; Thai Bao Tran; Toshiki Naito
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, TAYLOR & FRANCIS LTD, 13巻, 1号, 掲載ページ 15-24, 出版日 2007年01月, 査読付, We study stability radii of higher order linear difference systems under multi-perturbations. A formula for complex stability radius of higher order linear difference systems under multi-perturbations is given. Then, for the class of positive systems, we prove that the complex stability radius and real stability radius of the system under multi-perturbations coincide and they are computed via a simple formula. These are extensions of corresponding results of Hinrichsen and Son, Hinrichsen et al., Ngoc and Son, and Pappas and Hinrichsen. An example is given to illustrate the obtained results.
研究論文（学術雑誌）, 英語 - On periodicizing functions
Toshiki Naito; Jong Son Shin
Bull. Korean Math. Soc., 43巻, 出版日 2006年, 査読付
研究論文（学術雑誌）, 英語 - Stability radii of positive linear functional differential systems in Banach spaces
Pham Huu Anh Ngoc; Nguyen Van Minh; Toshiki Naito
International J. of Evolution Equations, 2巻, 1号, 出版日 2006年, 査読付
研究論文（学術雑誌）, 英語 - A spectral countability condition for almost automorphy of solutions of differential equations
Nguyen Van Minh; Toshiki Naito; Gaston Nguerekata
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, AMER MATHEMATICAL SOC, 134巻, 11号, 掲載ページ 3257-3266, 出版日 2006年, 査読付, We consider the almost automorphy of bounded mild solutions to equations of the form
(*) dx/dt = A(t)x+f(t)
with (generally unbounded) tau-periodic A(center dot) and almost automorphic f(center dot) in a Banach space X. Under the assumption that X does not contain c(0), the part of the spectrum of the monodromy operator associated with the evolutionary process generated by A(center dot) on the unit circle is countable. We prove that every bounded mild solution of (*) on the real line is almost automorphic.
研究論文（学術雑誌）, 英語 - Global optimization problems in stability analysis of linear dynamical systems
Pham Huu Anh Ngoc; Toshiki Naito; Jong Son Shin
POSITIVE SYSTEMS, PROCEEDINGS, SPRINGER-VERLAG BERLIN, 341巻, 掲載ページ 311-318, 出版日 2006年, 査読付, We deal with problems of maximizing the norm of the transfer matrix function of linear dynamical systems. It is shown that if a linear system is positive and (exponentially) asymptotically stable then the norm of its transfer matrix function attains the maximum at a specific point on the boundary of the stable region. For sake of space, exposure is kept to minimum in this paper. Two examples are given to illustrate the obtained results.
研究論文（学術雑誌）, 英語 - A characterization of solutions in linear differential equations with periodic forcing functions
J Kato; T Naito; JS Shin
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, TAYLOR & FRANCIS LTD, 11巻, 1号, 掲載ページ 1-19, 出版日 2005年01月, 査読付, We deal with periodic linear inhomogeneous differential equations of the form d x /d t = Ax ( t )+ f ( t ), where A is an m x m matrix and f a tau-periodic continuous function. The solutions of this equation will be characterized as a sum of tau-periodic functions and exponential-like functions in an explicit form. As applications of this result, we can obtain the complete classification of the set of initial values according to the behavior of solutions: bounded solutions on [0, infinity], tau-periodic solutions, quasi-periodic solutions, asymptotically periodic solutions and solutions with the growth order as t -->infinity , etc. The essential part of our method is to give a specific representation of the solutions of difference equations corresponding to the above equations.
研究論文（学術雑誌）, 英語 - Periodic solutions of evolution equations
K Ezzinbi; T Naito; N Minh; J Liu
DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, WATAM PRESS, 11巻, 5-6号, 掲載ページ 601-613, 出版日 2004年10月, 査読付, Consider the following evolution equations without delay or with finite or infinite delay in a general Banach space X,
u'(t) + A(t)u(t) = f (t, u(t)), t > 0,
u'(t) + A(t)u(t) = f (t, u(t), u(t)), t > 0.
We will analyze some fixed point theorems and then see how they can be applied to derive periodic solutions for the above mentioned equations.
研究論文（学術雑誌）, 英語 - On the Asymptotic Periodic Solutions of Abstract Functional Differential Equations
Takeshi Nishikawa; Nguyen Van Minh; Toshiki Naito
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, KOBE UNIV, DEPT MATHEMATICS, 47巻, 2号, 掲載ページ 307-327, 出版日 2004年08月, 査読付, The paper is concerned with conditions for all mild solutions of abstract functional differential equations with finite delay in a Banach space to be periodic and asymptotic periodic, where forcing term is a continuous 1-periodic function. The obtained results extend various recent ones on the subject.
研究論文（学術雑誌）, 英語 - Massera's theorem for almost periodic solutions of functional differential equations
S Murakami; T Naito; N Van Minh
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, MATH SOC JAPAN, 56巻, 1号, 掲載ページ 247-268, 出版日 2004年01月, 査読付, The Massera Theorem for almost periodic solutions of linear periodic ordinary differential equations of the form (*) x' = A(t)x + f(t), where f is almost periodic, is stated and proved. Furthermore, it is extended to abstract functional differential equations (**) x' = Ax + F(t)x(1) + f(t), where A is the generator of a compact semigroup, F is periodic and f is almost periodic. The main techniques used in the proofs involve a new variation of constants formula in the phase space and a decomposition theorem for almost periodic solutions.
研究論文（学術雑誌）, 英語 - Massera criterion for abstract functional differential equations with advance and delay
Takeshi Nishikawa; Nguyen Van Minh; Toshiki Naito
Applicable Analysis, 83巻, 11号, 掲載ページ 1171-1185, 出版日 2004年, 査読付
英語 - Bounded and periodic solutions of infinite delay evolution equations
J Liu; T Naito; N Van Minh
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, ACADEMIC PRESS INC ELSEVIER SCIENCE, 286巻, 2号, 掲載ページ 705-712, 出版日 2003年10月, 査読付, For A (t) and f (t, x, y) T-periodic in t, we consider the following evolution equation with infinite delay in a general Banach space X:
u'(t) + A(t)u(t) = f (t, u(t), u(t)), t > 0, u(s) = phi(s), s less than or equal to 0, (0.1)
where the resolvent of the unbounded operator A(t) is compact, and u(t) (s) = u(t + s), s less than or equal to 0. By utilizing a recent asymptotic fixed point theorem of Hale and Lunel (1993) for condensing operators to a phase space C-g, we prove that if solutions of Eq. (0.1) are ultimate bounded, then Eq. (0.1) has a T-periodic solution. This extends and improves the study of deriving periodic solutions from boundedness and ultimate boundedness of solutions to infinite delay evolution equations in general Banach spaces; it also improves a corresponding result in J. Math. Anal. Appl. 247 (2000) 627-644 where the local strict boundedness is used. (C) 2003 Elsevier Inc. All rights reserved.
研究論文（学術雑誌）, 英語 - Asymptotic properties and initial values of solutions to periodic linear equations
Junji Kato; Toshiki Naito; Jong Son Shin
数理解析研究所講究録 1309, 京都大学数理解析研究所, 1309巻, 掲載ページ 100-107, 出版日 2003年
研究論文（大学，研究機関等紀要）, 英語 - Boundedness and almost periodicity of solutions of partial functional differential equations
T Furumochi; T Naito; N Van Minh
JOURNAL OF DIFFERENTIAL EQUATIONS, ACADEMIC PRESS INC ELSEVIER SCIENCE, 180巻, 1号, 掲載ページ 125-152, 出版日 2002年03月, 査読付, We study necessary and sufficient conditions for the abstract functional differential equation (x) over dot = Ax + Fx(i) + f (t) to have almost periodic, quasi periodic solutions with the same structure of spectrum as f. The main conditions are stated in terms of the imaginary solutions of the associated characteristic equations and the spectrum of the forcing term f. The obtained results extend recent results to abstract functional differential equations. (C) 2002 Elsevier Science (USA).
研究論文（学術雑誌）, 英語 - A variation-of-constants formula for abstract functional differential equations in the phase space
Y Hino; S Murakami; T Naito; N Van Minh
JOURNAL OF DIFFERENTIAL EQUATIONS, ACADEMIC PRESS INC ELSEVIER SCIENCE, 179巻, 1号, 掲載ページ 336-355, 出版日 2002年02月, 査読付, For linear functional differential equations with infinite delay in a Banach space, a variation-of-constants formula is established in the phase space. As an application one applies it to study the admissibility of some spaces of functions whose spectra are contained in a closed subset of the real line, (C) 2002 Elsevier Science.
研究論文（学術雑誌）, 英語 - A Massera type theorem for functional differential equations with infinite delay
Toshiki Naito; Nguyen Van Minh; Jong Son Shin
Japanese Journal of Mathematics, 28巻, 1号, 掲載ページ 31-49, 出版日 2002年, 査読付
研究論文（学術雑誌）, 英語 - Existence of bounded solutions to lindear differential equations, (I)
Tohiki Naito; Jong Son Shin
数理解析研究所講究録, 1254巻, 掲載ページ 64-72, 出版日 2002年
研究論文（大学，研究機関等紀要）, 英語 - Spectrum and (almost) periodic solutions of functional differential equations
Toshiki Naito; Nguyen Van Minh; Jong Son Shin
Springer, Vietnam Journal of Mathematics, 30巻, SI号, 掲載ページ 577-589, 出版日 2002年, 査読付
研究論文（国際会議プロシーディングス）, 英語 - Bounded solutions and periodic solutions to linear differential equations in Banach spaces
Junji Kato; Toshik Naito; Jong Son Shin
Springer, Vietnam Journal of Mathematics, 30巻, SI号, 掲載ページ 561-575, 出版日 2002年, 査読付
研究論文（国際会議プロシーディングス）, 英語 - Periodic and almost periodic solutions of functional differential equations with finite and infinite delay
T Naito; N Van Minh; JS Shin
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, PERGAMON-ELSEVIER SCIENCE LTD, 47巻, 6号, 掲載ページ 3989-3999, 出版日 2001年08月, 査読付, We survey some new methods and results on periodic and almost periodic solutions of differential equations in Banach spaces.
研究論文（学術雑誌）, 英語 - New spectral criteria for almost periodic solutions of evolution equations
T Naito; N Van Minh; JS Shin
STUDIA MATHEMATICA, POLISH ACAD SCIENCES INST MATHEMATICS, 145巻, 2号, 掲載ページ 97-111, 出版日 2001年, We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form (x) over dot = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where e(i sp(f)) may intersect the spectrum of the monodromy operator P of (*) there sp(f) denotes the Carleman spectrum of (f). We show that if (*) has a bounded uniformly continuous mild solution u and sigma (Gamma)(P)\e(isp(f)) is closed, where sigma (Gamma)(P) denotes the part of sigma (P) on the unit circle, then (*) has a bounded uniformly continuous mild solution w such that e(i sp(w)) = e(i sp(f)). Moreover, w is a "spectral component" of u. This allows us to solve the general Massera-type problem for almost periodic solutions. Various spectral criteria for the existence of almost periodic and quasi-periodic mild solutions to (*) are given.
研究論文（学術雑誌）, 英語 - Existence and uniqueness of periodic solutions to periodic linear functional differential equations with finite delay
Jong Son Shin; Toshiki Naito; Nguyen Van Minh
Funkcialaj Ekvacioj, 44巻, 掲載ページ 53-71, 出版日 2001年
英語 - Periodic solutions of linear differential equatiions
Toshiki Naito; Jong Song Shin; Nguyen Van Minh
数理解析研究所講究録, 1216巻, 掲載ページ 78-89, 出版日 2001年
研究論文（大学，研究機関等紀要）, 英語 - Boundedness and almost periodicity in dynamical systems
T Naito; NV Minh; R Miyazaki; Y Hamaya
JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, TAYLOR & FRANCIS LTD, 7巻, 4号, 掲載ページ 507-527, 出版日 2001年, 査読付, We consider spectral criteria for the existence of bounded solutions to difference equations of the form x(n+1) = Ax(n) + f(n) with specific spectral properties. The results will be then applied to find periodic, almost periodic solutions to dx/dt = A(t)x +f(t)(*) and dx/dt = Ax + F(t)x(i) + f(t)(**) with (in general, unbounded) tau -periodic A(.), tau -periodic F(t),f(.). This provides a new and simple approach to find spectral criteria for the existence of periodic, almost periodic solutions to differential equations (*), (**).
研究論文（学術雑誌）, 英語 - Evolution semigroups and sums of commuting operators: A new approach to the admissibility theory of function spaces
S Murakami; T Naito; N Van Minh
JOURNAL OF DIFFERENTIAL EQUATIONS, ACADEMIC PRESS INC, 164巻, 2号, 掲載ページ 240-285, 出版日 2000年07月, This payer is concerned with conditions for the admissibility of a translation invariant function space M with respect to a well posed linear evolution equation du/dt = Au + f(t), t is an element of R (*). We propose a new approach to this problem by considering the sum of two commuting operators - d/dt : = - D-M and the operator of multiplication by A on M. On the one hand, the closure of this operator is the infinitesimal generator of the so-called evolution semigroup associated with (*). On the other hand, the generator G of this semigroup relates a mild solution u of (*) to the forcing term f by the rule Gu = -f. Consequently, various spectral criteria of the type sigma(D-M) boolean AND sigma(A) = circle divide for the admissibility of the function space M with respect to (*) can be proved in an elegant manner. Moreover, they can be naturally extended to general classes of differential equations, including higher order and abstract functional differential equations. Applications and examples are provided to illustrate the obtained results. (C) 2000 Academic Press.
研究論文（学術雑誌）, 英語 - Spectral analysis of an operator associated with linear functional differential equations and its applications
Satoru Murakami; Toshiki Naito; Nguyen Van Minh
EJQTDE, Prod. 6th coll. QTDE, 20号, 掲載ページ 1-15, 出版日 2000年
英語 - A decomposition theorem for bounded solutions and the existence of periodic solutions of periodic differential equations
T Naito; N Van Minh; R Miyazaki; JS Shin
JOURNAL OF DIFFERENTIAL EQUATIONS, ACADEMIC PRESS INC ELSEVIER SCIENCE, 160巻, 1号, 掲載ページ 263-282, 出版日 2000年01月, We prove a decomposition theorem fbr bounded uniformly continuous mild solutions to tau-periodic evolution equations of the form dx/dt = A(t) x + f(t) (*) with (in general, unbounded) tau-periodic A(.), tau-periodic f(.), and compact monodromy operator. By this theorem, every bounded uniformly continuous mild solution to (*) is a sum of a tau-periodic solution to (*) and a quasi periodic solution to its homogeneous equation. An analog of this for bounded solutions has been proved for abstract functional differential equations dx/dt = Ax + F(t) x(t) + f(t) with finite delay, where A generates a compact semigroup, As an immediate consequence, the existence of such a solution implies the existence of a tau-periodic solution to the inhomogeneous equation as well as a formula for its Fourier coefficients. This, even for the classical case of equations, improves considerably the previous results on the subject. (C) 2000 Academic Press.
研究論文（学術雑誌）, 英語 - Uniqueness of periodic solutions to periodic functional differential equations with finite delay
Toshiki Naito; Jong Son Shin
数理解析研究所講究録, 1128巻, 掲載ページ 28-36, 出版日 2000年
研究論文（大学，研究機関等紀要）, 英語 - On the spectrum of some functional differential equations
T Naito; N Van Minh; JS Shin
SEMIGROUPS OF OPERATORS: THEORY AND APPLICATIONS, BIRKHAUSER VERLAG AG, 42巻, 掲載ページ 222-228, 出版日 2000年
研究論文（国際会議プロシーディングス）, 英語 - On stability of linear autonomous functional differential equations
Jong Son Shin; Toshi Naito; Nguyen Van Minh
Funkcialaj Ekvacioj,43, 掲載ページ 323-337, 出版日 2000年
英語 - Periodic solutions of linear differential equations
Toshiki Naito; Jong; Song Shin; Nguyen Van Minh
出版日 2000年
英語 - Existence and continuous dependence of mild solutions to semilinear functional differential equations in banach spaces
JS Shin; T Naito
TOHOKU MATHEMATICAL JOURNAL, TOHOKU UNIVERSITY, 51巻, 4号, 掲載ページ 555-583, 出版日 1999年12月, This paper is concerned with a general existence and continuous dependence of mild solutions to semilinear functional differential equations with infinite delay in Banach spaces. In particular, our results are applicable to the equations whose Cg-semigroups and nonlinear operators, defined on an open set, are noncompact.
研究論文（学術雑誌）, 英語 - Semi-Fredholm operators and periodic solutions for linear functional differential equations
JS Shin; T Naito
JOURNAL OF DIFFERENTIAL EQUATIONS, ACADEMIC PRESS INC ELSEVIER SCIENCE, 153巻, 2号, 掲載ページ 407-441, 出版日 1999年04月, We deal with the inhomogeneous linear periodic equation with infinite delay of the form dx/dt = Ax(t) + B(t, x(t)) + F(t), where A is the generator of a C-0-semigroup on a Banach space. Assuming that it has a bounded solution, we obtain several criteria on the existence and the uniqueness of periodic solutions for the equation in the general phase space B and in the concrete phase space B = UCg. The key of our approach is the employment of the perturbation theory of semi-Fredholm operators to show that the period map satisfies the condition of the fixed point theorem by Chow and Hair (Funkcial. Ekvac. 17 (1974), 31-38). (C) 1999 Academic Press.
研究論文（学術雑誌）, 英語 - Evolution semigroups and spectral criteria for almost periodic solutions of periodic evolution equations
T Naito; N Van Minh
JOURNAL OF DIFFERENTIAL EQUATIONS, ACADEMIC PRESS INC, 152巻, 2号, 掲載ページ 358-376, 出版日 1999年03月, We investigate spectral criteria for the existence of(almost) periodic solutions to linear I-periodic evolution equations of the Form dx/dt = A (t) x + f(t) with (in general, unbounded) A(t) and (almost) periodic f. Using the evolution semigroup associated with the evolutionary process generated by the equation under consideration we show that if the spectrum of the monodromy operator does not intersect the set <(e(isp(f)))over bar>, then the above equation has an almost periodic (mild) solution x(f) which is unique if one requires sp(x(f)) subset of <(lambda+2 pi k, k is an element of Z, lambda is an element of sp(f)})over bar>. We emphasize that our method allows us to treat the equations without assumption on the existence of Floquet representation. This improves recent results on the subject. In addition we discuss some particular cases, in which the spectrum of monodromy operator does not intersect the unit circle, and apply the obtained results to study the asymptotic behavior of solutions. Finally, an application to parabolic equations is considered. (C) 1999 Academic Press.
研究論文（学術雑誌）, 英語 - On stability of solutions in linear autonomous functional differenteal equations
John Son Shin; Toshiki Naito; Nguyen Van Minh
数理解析研究所講究録, 掲載ページ 231-242, 出版日 1999年
研究論文（大学，研究機関等紀要）, 英語 - On a spectral criterion for almost periodicity of solutions to periodic evolutions equatons
Toshiki Naito; Nguyen Van Minh
Electric Journal of Qualitative Theory of Differential Equations,1, 掲載ページ 1-28, 出版日 1999年
研究論文（学術雑誌）, 英語 - Evokution semigroups and harmonic analysis of bounded solutions of evolution equations
Toshiki Naito; Nguyen Van Minh; Jong Son Shin
Surikaisekikenkyusho Kokyuroku,1083, 掲載ページ 166-168, 出版日 1999年
英語 - Spectral criteria for almost periodicity of solutions of periodic evolution equations(共著)
T. Naito; Nguyen V.M
数理解析研究所講究録, 京都大学, 1034巻, 掲載ページ 49-51, 出版日 1998年
研究論文（大学，研究機関等紀要）, 英語 - Existence of periodic solutions for periodic linear functional differential equations in Banach Spaces(共著)
J.S. Shin; T. Naito
数理解析研究所講究録, 掲載ページ 120-129, 出版日 1998年
研究論文（大学，研究機関等紀要）, 英語 - The generator of the solution semigroup for the general ilnear functional differential equation
Jong Son Shin; Toshiki Naito; Nguyen Van Minh
Bulletin of the University of Electro-Communications,11-1, 掲載ページ 29-38, 出版日 1998年
研究論文（大学，研究機関等紀要）, 英語 - On solution semigroups of general functional differential equations(共著)
T Naito; JS Shin; S Murakami
Nonlinear Analysis, Theory, Method & Applications, PERGAMON-ELSEVIER SCIENCE LTD, 30巻, 7号, 掲載ページ 4565-4576, 出版日 1997年12月
研究論文（学術雑誌）, 英語 - 無限の遅れをもつ発展方程式
数理解析研究所講究録, 984号, 掲載ページ 147-160, 出版日 1997年
研究論文（大学，研究機関等紀要）, 英語 - On solution semigroups of furctional differential equations
数理解析研究所講究録, 940号, 掲載ページ 161-175, 出版日 1996年
研究論文（大学，研究機関等紀要）, 英語 - Fading memory spaces and stability properties for functional differential equations with infinite delay
Funkcialaj Ekvacioj, 掲載ページ 32, 出版日 1989年
研究論文（学術雑誌）, 英語 - Adjoint semigroups associated with linear functional differential equations with infinite delay
Toshiki Naito
Finite and Infinite Dimensional Dynamics, Lecture Notes in Numerical and Applied Analysis, Vol. 15, Kinokuniya, Tokyo, 掲載ページ 165-185, 出版日 1988年08月, 査読付
研究論文（国際会議プロシーディングス）, 英語 - A modified form of the variation-of-constants formula for equations with infinite delay
Tohoku Mathematical Journal, 掲載ページ 36, 出版日 1984年
研究論文（学術雑誌）, 英語 - On linear autonomous retarded equations with an abstract phase space for infinite delay
Journal of Differential Equations, 掲載ページ 33, 出版日 1979年
研究論文（学術雑誌）, 英語 - On autonomous linear functional differential equations with infinite retardations
Journal of Differential Equations, 掲載ページ 21, 出版日 1976年
研究論文（学術雑誌）, 英語
MISC
書籍等出版物
- 初等常微分方程式の解法
内藤敏機; 申正善
日本語, 共著, 牧野書店, 出版日 2005年11月 - 理工系基礎数学演習
石田晴久; 伊藤裕也; 大野真裕; 木田雅成; 田吉隆夫; 内藤敏機; 山口耕平; 山田裕一
日本語, 共著, 昭晃堂, 出版日 2005年04月 - タイムラグをもつ微分方程式
内藤敏機; 原惟行; 日野義之; 宮崎倫子
日本語, 共著, 第５章 線形関数微分方程式, 牧野書店, 出版日 2002年11月 - Almost Periodic Solutions of Differential Equations in Banach Spaces
Yoshiyuki Hino; Toshiki Naito; Nguyen Van Minh; Jong Son Shin
英語, 共著, Taylor and Francis,, 出版日 2002年 - Dual Semigroups Associated with Linear Functional Differential Equations with Infinite Delay
英語, International Conference on Differential Equations Barcelona 1991, World Scientific, 出版日 1993年 - Functional Differential Equations with Infinite Delay
Yoshiyuki Hino; Satoru Murakami; Toshiki Naito
英語, 共著, Springer-Verlag, 出版日 1991年 - Asymptotic stability of linear fanctional differential equations with the fadeng memory space
英語, Proc International symposium Functional Differential Equations, Kyoto 1990, World Scientific, 出版日 1991年