Dichotomy and almost automorphic solution of difference system

Castillo, Samuel; Pinto, Manuel

doi:10.14232/ejqtde.2013.1.32

Cited by 10 publications

(8 citation statements)

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“…• Using a different approach we improve the existence results of [21]. Furthermore, our results also extend the results of [11] and [22] in the particular time scale T = Z.…”

Section: Introductionsupporting

confidence: 71%

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Almost automorphic solutions of delayed neutral dynamic systems on hybrid domains

Adıvar

Koyuncuoğlu

Raffoul

2016

APPL ANAL DISCRETE M

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We study the existence of almost automorphic solutions of the delayed neutral dynamic system on hybrid domains that are additively periodic. We use exponential dichotomy and prove the uniqueness of projector of exponential dichotomy to obtain some limit results leading to sufficient conditions for existence of almost automorphic solutions to neutral system. Unlike the existing literature we prove our existence results without assuming boundedness of the coefficient matrices in the system. Hence, we significantly improve the results in the existing literature. Finally, we also provide an existence result for almost periodic solutions of the system.

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“…• Using a different approach we improve the existence results of [21]. Furthermore, our results also extend the results of [11] and [22] in the particular time scale T = Z.…”

Section: Introductionsupporting

confidence: 71%

“…Almost automorphic solutions of difference equations have been investigated in [5], [11] and [22]. In addition, C. Lizama and J. G. Mesquita generalized the notion of almost automorphy in [21] by studying almost automorphic solutions of dynamic equations on time scales that are invariant under translation.…”

Section: Introductionmentioning

confidence: 99%

Almost automorphic solutions of delayed neutral dynamic systems on hybrid domains

Adıvar

Koyuncuoğlu

Raffoul

2016

APPL ANAL DISCRETE M

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“…Moreover, we recall that N'Guérékata has given a huge impulse to the study of almost automorphic solutions of differential equations [1,7,12,14,15,21,23,25,26]. For some recent results of almost automorphic differential equations consult also [5,6].…”

Section: Introductionmentioning

confidence: 99%

Almost automorphic delayed differential equations and Lasota-Wazewska model

Coronel¹,

Maulén²,

Pinto³

et al. 2017

Discrete &Amp; Continuous Dynamical Systems - A

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Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and uniqueness of almost automorphic solutions are given.Date: August 1, 2018. Key words and phrases. Abstract delay differential equations, Almost automorphic, Exponential dichotomy, Ergodicity, Evolution operator.

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“…Furthermore, in [26] C. Lizama and J. G. Mesquita perfectly generalized the notion of almost automorphy by studying of almost automorphic solutions of dynamic equations on time scales that are invariant under translation. In [15], S. Castillo and M. Pinto studied almost automorphic solutions of the system with constant coefficient matrix A y (n + 1) = Ay (n) + f (n) using (µ 1 , µ 2 )-exponential dichotomy. In [29] I. Mishra et al investigated almost automorphic solutions to functional differential equation…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Almost automorphic solutions of discrete delayed neutral system

Adıvar

Koyuncuoğlu

2016

Journal of Mathematical Analysis and Applications

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We study almost automorphic solutions of the discrete delayed neutral dynamic systemby means of a fixed point theorem due to Krasnoselskii. Using discrete variant of exponential dichotomy and proving uniqueness of projector of discrete exponential dichotomy we invert the equation and obtain some limit results leading to sufficient conditions for the existence of almost automorphic solutions of the neutral system. Unlike the existing literature we prove our existence results without assuming boundedness of inverse matrix A (t) −1 . Hence, we significantly improve the results in the existing literature. We provide two examples to illustrate effectiveness of our results. Finally, we also provide an existence result for almost periodic solutions of the system.

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Dichotomy and almost automorphic solution of difference system

Cited by 10 publications

References 0 publications

Almost automorphic solutions of delayed neutral dynamic systems on hybrid domains

Almost automorphic solutions of delayed neutral dynamic systems on hybrid domains

Almost automorphic delayed differential equations and Lasota-Wazewska model

Almost automorphic solutions of discrete delayed neutral system

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