%0 Journal Article
%T Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Liu, Z.
%A Wu, Z.
%A Ume, J. S.
%A Kang, S. M.
%D 2015
%\ 04/01/2015
%V 41
%N 2
%P 389-405
%! Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation
%K Uncountably many bounded
positive solutions
%K second order nonlinear neutral delay partial
difference equation
%K Banach fixed point theorem
%R
%X 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.
%U http://bims.iranjournals.ir/article_618_f85997965fd591bde2437b36149d7fd1.pdf