Asymptotically omega-periodic solutions for a system of differential equations with mixed delays

Abstract

In this work, some criteria are established for the existence of asymptotically $w$-periodic solutions for a system of differential equations with mixed delays which arises in neural networks (NNs) theory. To do so, the properties of $w$-periodic limit functions and the Schauder fixed point theorem are used. The forcing term (including the activation functions) is assumed to be H{\"o}lder continuous. Our results are new since the condition of Lipschitz on the forcing term is not required.