Variational approach to the existence of solutions for non-instantaneous impulsive differential equations with perturbation

TL;DR

This paper uses a variational method to prove the existence of solutions for a class of second-order impulsive differential equations with perturbations, under specific growth conditions on nonlinearities.

Contribution

It introduces a variational framework to establish solution existence for impulsive differential equations with perturbations, considering super-quadratic and sub-quadratic nonlinearities.

Findings

Existence of at least one solution under given conditions

Applicable to second-order impulsive differential equations with perturbations

Utilizes variational methods for proof

Abstract

In this paper, we study the existence of solutions for second-order non-instantaneous impulsive differential equations with a perturbation term. By variational approach, we obtain the problem has at least one solution under assumptions that the nonlinearities are super-quadratic at infinity, and sub-quadratic at the origin.