Almost automorphic solutions of discrete delayed neutral system

作者：Adivar Murat^*; Koyuncuoglu Halis Can

来源：Journal of Mathematical Analysis and Applications, 2016, 435(1): 532-550.

DOI：10.1016/j.jmaa.2015.10.056

• Almost automorphic
• Almost periodic
• Discrete exponential dichotomy
• Discrete nonlinear neutral system
• Krasnoselskii
• Unique projection

We study almost automorphic solutions of the discrete delayed neutral dynamic system
x(t + 1) = A(t)x(r) + Delta Q(t, x(t - g(t)) + G(t, x(t), x(t - g(t))
by 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.

• 出版日期2016-3-1