Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X41220150401Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation389405618ENZ.LiuLiaoning Normal UniversityZ.WuLiaoning Normal UniversityJ. S.UmeDepartment of Mathematics, Changwon National UniversityS. M.KangGyeongsang National UniversityJournal Article20131209In this paper we consider the second order nonlinear <br />neutral delay partial difference equation <br />$\Delta_n\Delta_m\big(x_{m,n}+a_{m,n}x_{m-k,n-l}\big)+ <br />f\big(m,n,x_{m-\tau,n-\sigma}\big)=b_{m,n}, m\geq m_{0},\, <br />n\geq n_{0}.$<br />Under suitable conditions, by making use of the Banach fixed point <br />theorem, we show the existence of uncountably many bounded <br />positive solutions for the above partial difference equation. <br />Three nontrivial examples are given to illustrate the advantages <br />of our results. <br /> http://bims.iranjournals.ir/article_618_f85997965fd591bde2437b36149d7fd1.pdf