Variational approach to second-order impulsive dynamic equations on time scales

TL;DR

This paper applies variational methods and critical point theory to establish existence results for nonlinear impulsive dynamic equations on time scales, including those with linear derivative dependence and impulsive conditions.

Contribution

It introduces a variational framework for impulsive dynamic equations on time scales, extending existence results to equations with linear derivative dependence and impulsive conditions.

Findings

Established conditions for the existence of solutions.

Extended variational methods to impulsive equations with derivative dependence.

Provided new insights into impulsive dynamic equations on time scales.

Abstract

The aim of this paper is to employ variational techniques and critical point theory to prove some conditions for the existence of solutions to nonlinear impulsive dynamic equation with homogeneous Dirichlet boundary conditions. Also we will be interested in the solutions of the impulsive nonlinear problem with linear derivative dependence satisfying an impulsive condition.