# Sequences of positive homoclinic solutions to difference equations with variable exponent

## TL;DR

This paper investigates the existence of infinitely many positive homoclinic solutions for a second-order difference equation involving a variable exponent p_k-Laplacian, using critical point theory and Ricceri's variational principle.

## Contribution

It introduces a novel approach to find multiple positive homoclinic solutions in difference equations with variable exponents using advanced variational methods.

## Key findings

- Proved existence of infinitely many positive homoclinic solutions
- Applied critical point theory to variable exponent difference equations
- Utilized Ricceri's variational principle effectively

## Abstract

We study the existence of infinitely many positive homoclinic solutions to a second-order difference equation on integers with $p_k$-Laplacian. To achieve our goal we use the critical point theory and the general variational principle of Ricceri.