Existence of Heteroclinic Solutions in Nonlinear Differential Equations of the Second-Order Incorporating Generalized Impulse Effects with the Possibility of Application to Bird Population Growth

Abstract

This work considers the existence of solutions of the heteroclinic type in nonlinear second-order differential equations with ϕ-Laplacians, incorporating generalized impulsive conditions on the real line. For the construction of the results, it was only imposed that ϕ be a homeomorphism, using Schauder’s fixed-point theorem, coupled with concepts of L1-Carathéodory sequences and functions along with impulsive points equiconvergence and equiconvergence at infinity. Finally, a practical part illustrates the main theorem and a possible application to bird population growth.

Keywords

• heteroclinic solutions
• impulsive points equiconvergence and equiconvergence at infinity
• <i>L</i>¹-Carathéodory sequences and functions