Multiple Solutions for Boundary Value Problems of p-Laplacian Difference Equations Containing Both Advance and Retardation

Zhenguo Wang,Zhan Zhou

doi:10.1155/2020/8342735

Abstract

This paper concerns the existence of solutions for the Dirichlet boundary value problems of p-Laplacian difference equations containing both advance and retardation depending on a parameter λ. Under some suitable assumptions, infinitely many solutions are obtained when λ lies in a given open interval. The approach is based on the critical point theory.

Highlights

Let Z and R be the sets of integers and real numbers, respectively
By means of critical point theory, many researchers devote themselves to the study of difference equations and achieve many excellent results, for example, the results on boundary value problems [4,5,6,7,8,9,10,11,12,13,14,15,16], periodic solutions [17,18,19,20,21,22], and homoclinic solutions [23,24,25,26,27,28,29,30,31] had been obtained
Zhou and Ling [10] studied the existence of infinitely many positive solutions for the following boundary value problem of the second order nonlinear difference equation with φc-Laplacian:

Summary

Introduction

Let Z and R be the sets of integers and real numbers, respectively. For a, b ∈ Z, Z(a, b) denotes the discrete interval {a, a + 1, . . . , b} if a ≤ b. We consider the following boundary value problem of difference equation containing both advance and retardation:. By means of critical point theory, many researchers devote themselves to the study of difference equations and achieve many excellent results, for example, the results on boundary value problems [4,5,6,7,8,9,10,11,12,13,14,15,16], periodic solutions [17,18,19,20,21,22], and homoclinic solutions [23,24,25,26,27,28,29,30,31] had been obtained. Zhou and Ling [10] studied the existence of infinitely many positive solutions for the following boundary value problem of the second order nonlinear difference equation with φc-Laplacian:. Two examples are given to illustrate our main results

Preliminaries

Main Results

Examples