TY - JOUR
ID - 618
TI - Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Liu, Z.
AU - Wu, Z.
AU - Ume, J. S.
AU - Kang, S. M.
AD - Liaoning Normal University
AD - Department of Mathematics, Changwon National University
AD - Gyeongsang National University
Y1 - 2015
PY - 2015
VL - 41
IS - 2
SP - 389
EP - 405
KW - Uncountably many bounded
positive solutions
KW - second order nonlinear neutral delay partial
difference equation
KW - Banach fixed point theorem
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_618.html
L1 - http://bims.iranjournals.ir/article_618_f85997965fd591bde2437b36149d7fd1.pdf
ER -