# Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation

Document Type : Research Paper

Authors

1 Liaoning Normal University

2 Department of Mathematics, Changwon National University

3 Gyeongsang National University

Abstract

In this paper we consider the second order nonlinear
neutral delay partial difference equation
$\Delta_n\Delta_m\big(x_{m,n}+a_{m,n}x_{m-k,n-l}\big)+ f\big(m,n,x_{m-\tau,n-\sigma}\big)=b_{m,n}, m\geq m_{0},\, n\geq n_{0}.$
Under suitable conditions, by making use of the Banach fixed point
theorem, we show the existence of uncountably many bounded
positive solutions for the above partial difference equation.
Three nontrivial examples are given to illustrate the advantages
of our results.

Keywords

Main Subjects

### History

• Receive Date: 09 December 2013
• Revise Date: 10 January 2014
• Accept Date: 05 March 2014