一类奇异二阶阻尼差分方程周期边值问题正解的存在性

研究了一类奇异二阶阻尼差分方程周期边值问题{Δ²x(t-1)+αΔx(t-1)+βx(t)=f(t,x(t), Δx(t-1)), t∈［1,T］_Z,x(0)=x(T), Δx(0)=Δx(T)正解的存在性,其中T >2是一个整数, α、 β均为常数, f(t,x,y):［1,T］_Z×(0,∞)×R→R关于(x,y)∈(0,∞)×R连续且允许f在x=0处奇异即lim_x→0⁺ f(t,x,y)=+∞,(t,y)∈［1,T］_Z×R。主要结果的证明基于Leray-Schauder非线性抉择。

Existence of positive solutions for periodic boundary conditions of singular second-order damped difference equations

This paper studies the existence of positive solutions for periodic boundary value problems of second order damped difference equations{Δ²x(t-1)+αΔx(t-1)+βx(t)=f(t,x(t), Δx(t-1)), t∈［1,T］_Z,x(0)=x(T), Δx(0)=Δx(T)where T >2 is an integer, α, β are constants, f(t,x,y):［1,T］_Z×(0,∞)×R→R is continuous with respect to (x,y)∈(0,∞)×R, f may be singular at x=0, which means that lim_x→0⁺ f(t,x,y)=+∞,(t,y)∈［1,T］_Z×R. The proof of main results is based on nonlinear alternative of Leray-Schauder.