On multiplicity of solutions to nonlinear partial difference equations with delay

Yong Zhou,Yanyun Zhao,Ahmed Alsaedi,Bashir Ahmad

doi:10.1186/s13662-018-1651-6

Abstract

In this paper, we present an existence criterion for multiple positive solutions of nonlinear neutral delay partial difference equations. Such equations can be regarded as a discrete analog of neutral delay partial differential equations. Our main result relies on fixed point index theory. An example is constructed to show the applicability of the obtained result.

Highlights

Partial difference equations constitute an important and interesting area of research in mathematics
We refer the reader to a series of papers [4,5,6,7,8,9,10] and the references therein, while some recent work on the oscillation and nonoscillation criteria for partial difference equations can be found in the articles [11,12,13,14,15,16,17,18]
The goal of this paper is to discuss the multiplicity of positive solutions of nonlinear neutral partial difference equation with the aid of the fixed point index theory

Summary

Introduction

Partial difference equations constitute an important and interesting area of research in mathematics. For some classical results concerning the solvability of some classes of partial difference equations, see [1]. Many researchers recently investigated solvability and oscillation criteria for partial difference equations with two variables. We refer the reader to a series of papers [4,5,6,7,8,9,10] and the references therein, while some recent work on the oscillation and nonoscillation criteria for partial difference equations can be found in the articles [11,12,13,14,15,16,17,18]. To the best of our knowledge, the topic of existence of multiple positive solutions for partial difference equations has yet to be addressed

Objectives

Conclusion