Almost automorphic solutions of discrete delayed neutral system

Abstract

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.

Existence results for integro-differential equations with reflection

“…Many authors have studied problems of existence of periodic, almost periodic and automorphic solutions for different kinds of differential and integral equations (cf. Adivar and Koyuncuoǧlu [1], Baskakov et al, [7], Bochner [10], N'Guérékata [23], and Papageorgiou et al [24,25]). For example, the function…”

Existence Results for Integro-Differential Equations with Reflection

“…Many authors have studied problems of existence of periodic, almost periodic and automorphic solutions for different kinds of differential and integral equations (cf. Adivar and Koyuncuoǧlu [1], Baskakov et al [2], Bochner [3], N'Gu er ekata [4], and Papageorgiou et al [5,6]). For example, the function…”

Almost Automorphic Solutions to Nonlinear Difference Equations

“…In the recent past, the theories of almost periodic and almost automorphic functions have taken prominent attention from scholars, and the existence of almost periodic and almost automorphic solutions of dynamic equations has become a hot research topic on time domains with continuous, discrete, and hybrid structures. We refer readers to the monographs [10,[12][13][14][15], papers [16][17][18][19][20][21][22][23][24][25][26][27], and references therein. Analysis of the linkage between the existence of bounded and periodic solutions of dynamic equations has always been an interesting research topic in applied mathematics.…”