一类p-Laplacian差分方程多个正解的存在性

Existence of multiple positive solutions of a class of p-Laplacian difference equations

考察p-Laplacian差分方程边值问题Δ[φp(Δu(t-1))]+a(t)f(u(t))=0,t∈[1,T+1],Δu(0)=u(T+2)=0的多解性,其中T为固定的正整数,φp(s)是p-Laplacian算子,φp(s)=|s|p-2s,p>1,(φp)-1=φq,1/p+1/q=1,且不要求lim l→0 f(l)/lp-1,lim l→∞f(l)/lp-1存在.

Abstract. The multiplicity of positive solutions for the following boundary-value problem of p-Laplacian difference equations was surveyed：△[φp（△u（t-1）]＋a（t）f（u（u（t））=0,t∈[1,T＋1]△u（0）=u（T＋2）=0where T is a fixed positive integerφ（s）-P-Laplacianoperator,,φp（s）=｜s｜^p-2,p〉1,（φp）^1=φq,1/p＋1/q=1,and the existence ofliml→0f（l）/l^p-1,liml→∞f（l）/lp-1is not required.