Solvability of second order coupled systems on the half-line

Abstract

In this work, we consider a second-order coupled system of differential equations in semiinfinite intervals. The arguments apply the fixed point theory, Green’s functions technique, L1-Carathéodory functions theory, a truncation technique, and Schauder’s fixed point theorem. The technique used consists in application of a Nagumo-type growth condition to nonlinearities and the concept of equiconvergence for recovering the compactness of the associated operators. In the last section, we present an example.