Existence result for impulsive coupled systems on the half-line

Abstract

This work considers a second order impulsive coupled system of differential equations with generalized jump conditions in half-line, which can depend on the impulses of the unknown functions and their first derivatives.The arguments apply the fixed point theory, Green's functions technique, L 1 -Carathéodory functions and sequences and Schauder's fixed point theorem.The method is based on Carathéodory concept of functions and sequences, together with the equiconvergence on infinity and on each impulsive moment, and it allows to consider coupled fully nonlinearities and very general impulsive functions.

First-order periodic coupled systems with generalized impulse conditions

“…Furthermore, results on equi-regulated functions are essential to deal with the discontinuities at the instants of impulse. A similar problem is studied in [19,20,21], and with similar techniques in [18,22].…”