Existence of bounded solutions near perturbed heteroclinics

Abstract

Here, we consider a planar differential equation with a perturbed hetero- clinic. We apply the exponential dichotomy theory and Lyapunov-Schmidt reduction method to provide a bifurcation function and sufficient conditions for the existence of a bounded solution near the perturbed heteroclinic. Finally, by an example, the results will be verified for a Newtonian system; however, the method is applicable for a wide range of systems including non-Hamiltonian ones.