一类一阶差分方程周期边值问题正解连通分支的振荡及无穷多个正解的存在性

Existence of infinite positive solutions and oscillation of connected component of positive solutions for a class of periodic boundary value problems of first order difference equation

本文研究了一类一阶差分方程周期边值问题-Δx(t)+q(t)x(t)=λa(t)x(t)+f(t,x(t)x(t)),t∈T^,x(0)=x(T)正解连通分支的振荡及无穷多个正解的存在性,其中λ>0是参数,T>2是整数,T^{0,1,…T-1},q:T^→[0,∞),a:T^→(0,∞),f:T^×R→R连续,f(t,0)=0.]主要结果的证明基于Rabinowitz全局分歧定理.

In this paper,we study the existence of infinite positive solutions and oscillation of connected component of positive solutions for the periodic boundary value problems of the first order difference equation-Δx(t)+q(t)x(t)=λa(t)x(t)+f(t,x(t)x(t)),t∈T^,x(0)=x(T),whereλ>0 is a parameter,T>2 is a integer,T^{0,1,…T-1},q:T^→[0,∞),a:T^→(0,∞),f:T^×R→R is continuous and f(t,0)=0]satisfies some conditions.The proof of the main results is based on the Rabinowitz global bifurcation theorems.