Small Solutions of the Perturbed Nonlinear Partial Discrete Dirichlet Boundary Value Problems with (p,q)-Laplacian Operator

Feng Xiong,Zhan Zhou

doi:10.3390/sym13071207

Abstract

In this paper, we consider a perturbed partial discrete Dirichlet problem with the (p,q)-Laplacian operator. Using critical point theory, we study the existence of infinitely many small solutions of boundary value problems. Without imposing the symmetry at the origin on the nonlinear term f, we obtain the sufficient conditions for the existence of infinitely many small solutions. As far as we know, this is the study of perturbed partial discrete boundary value problems. Finally, the results are exemplified by an example.

Highlights

Let Z and R denote the sets of integers and real numbers, respectively
Inspired by the above research, we found that the perturbed partial difference equations had rarely been studied, so this paper aims at studying small solutions of the perturbed partial discrete Dirichlet problems with the ( p, q)-Laplacian operator
We studied the existence of small solutions of perturbed partial discrete

Summary

Introduction

Let Z and R denote the sets of integers and real numbers, respectively. We consider the following partial discrete problem, namely ( D λ,μ ). Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Objectives

Results

Conclusion