Existence of positive solutions for certain nonlinear partial difference equations

Authors:
B. G. Zhang;Yong Zhou;Y. Q. Huang
Affiliations:
Department of Mathematics, Ocean University of China Qingdao 266071, P.R. China;Department of Mathematics, Xiangtan University Xiangtan, Hunan 411105, P.R. China;Department of Mathematics, Xiangtan University Xiangtan, Hunan 411105, P.R. China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2003

Citing 6
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Abstract

In this paper, we consider nonlinear partial difference equations of the form @D"n^h@D"m^r (x"m","n - cx"m"-"k","n"-"l) + (-1)^h^+^r^+^1Pm,n@?(x"m"-"@t","n"-"@d) = 0, where c@eR, h,r,k,l @e N^+, @t,@d @e N, {Pm,n} m = m"0~,~, n = n"0is a double sequence of real numbers and @? @e C(R, R). We obtain sufficient conditions for the existence of positive solutions of this equation using Knaster's fixed-point theorem.