First-order periodic coupled systems with generalized impulse conditions

Abstract

We present some existence and localization results for periodic solutions of impulsive first-order coupled non-linear systems of two equations, without requiring periodicity for the nonlinearities. The arguments are based on Schauder’s Fixed Point Theorem together with the upper and lower solution method, where the upper and lower solutions are not necessarily well-ordered. In addition, results on equi-regulated functions are required for the impulsive analysis. An application to a Wilson-Cowan system of two strongly coupled neurons illustrates one of the main results.