Almost automorphic solutions of delayed neutral dynamic systems on hybrid domains

Almost Automorphic Solutions of Difference Equations

We study discrete almost automorphic functions sequences defined on the set of integers with values in a Banach space X. Given a bounded linear operator T defined on X and a discrete almost automorphic function f n , we give criteria for the existence of discrete almost automorphic solutions of the linear difference equation Δu n Tu n f n . We also prove the existence of a discrete almost autom...

On almost automorphic solutions of linear operational-differential equations

for each t ∈R. When convergence in (1.1) and (1.2) is uniform in t ∈ R, f is said to be (Bochner) almost periodic. Almost periodic functions are characterized by the following so-called Bochner’s criterion. f : R→ X is almost periodic if and only if for every sequence of real numbers (s′ n), there exists a subsequence (sn) such that (f (t+sn)) is uniformly convergent in t ∈R. For more informati...

Existence of Pseudo Almost Automorphic Solutions for the Heat Equation with Sp-Pseudo Almost Automorphic Coefficients

Asymptotic almost automorphic solutions of impulsive neural network with almost automorphic coefficients

In this paper existence and asymptotic stability of asymptotically almost automorphic solution of impulsive neural networks with delay is discussed. The results are established by using various fixed point theorems and Lyapunov-like functional. As far as we know, this is the first paper to discuss such kind of solutions for impulsive neural networks. At the end, we give few examples to illustra...

Asymptotically almost automorphic solutions of fractional order neutral integro-differential equations

In this paper, we study the existence of asymptotic almost automorphic solution of fractional neutral integro-differential equation. We prove the result by using fixed point theorems. We show the result with Lipschitz condition and without Lipschitz condition on the forcing term. Finally examples are given to illustrate the analytical findings. Mathematics Subject Classification(2010): 34A08, 1...