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

Author:

de Sousa Robert12ORCID,Fernandes Marco António de Sales Monteiro1ORCID

Affiliation:

1. Núcleo de Matemática e Aplicações (NUMAT), Centro de Investigação em Ciências Exatas (CiCE), Faculdade de Ciências e Tecnologia, Universidade de Cabo Verde, Praia 7943-010, Cabo Verde

2. Centro de Investigação em Matemática e Aplicações (CIMA), Universidade de Évora, Rua Romão Ramalho, 59, 7000-671 Évora, Portugal

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.

Publisher

MDPI AG

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