Positive solutions and eigenvalue intervals for a second order p-Laplacian discrete system

Jin Zhao

doi:10.1186/s13662-018-1744-2

Abstract

In this paper, we investigate the existence of at least one positive solution to a second order p-Laplacian discrete system. As applications, we characterize the eigenvalue intervals for one typical n-dimensional system. The proof is based on a well-known fixed point theorem in cones.

Highlights

We investigate the existence of at least one positive solution for the second order p-Laplacian discrete boundary value system
The discrete boundary value problems arise in different fields of research
We prove that system (2) has at least one positive solution for each λ in an explicit eigenvalue interval

Summary

Introduction

We investigate the existence of at least one positive solution for the second order p-Laplacian discrete boundary value system. The discrete boundary value problems arise in different fields of research. Different types of discrete boundary value problems have been studied in the past three decades, here we refer the reader to [1, 2, 4, 5, 7, 8, 15, 19]. Several eigenvalue characterizations for different kinds of boundary value problems have appeared, and we refer the reader to [5, 12, 14, 16, 18]. Some results on the existence of at least one positive solution to system (1) are established in Sect.

Preliminaries

Conclusions