Heteroclinic and homoclinic solutions for nonlinear second-order coupled systems with $$\phi $$-Laplacians

Abstract

In this paper, we present sufficient conditions for the existence of heteroclinic or homoclinic solutions for second-order coupled systems of differential equations on the real line. We point out that it is required only conditions on the homeomorphisms and no growth or asymptotic conditions are assumed on the nonlinearities. The arguments make use of the fixed point theory, \(L^{1}\)-Carathéodory functions and Schauder’s fixed point theorem. An application to a family of second-order nonlinear coupled systems of two degrees of freedom, shows the applicability of the main theorem.