一类非线性三阶差分方程正周期解的存在性和多解性

Existence and multiplicity of positive periodic solutions for a class of nonlinear third-order difference equations

考虑一类非线性三阶差分方程Δ^(3)u(t-3)+αΔ^(2)u(t-2)+βΔu(t-1)=f(t,u(t)),t∈[3,T]Z正周期解的存在性和多解性,其中T>4,α>0,-1<β<0,f:[3,T]_(Z)×[0,∞)→R关于u∈[0,∞)连续,f(t+ω,u)=f(t,u),ω∈Z^(+)。主要结果的证明基于Guo-Krasnosel'skii不动点定理。

This paper considers the existence and multiplicity of positive periodic solutions for a class of nonlinear third-order difference equationΔ^(3)u(t-3)+αΔ^(2)u(t-2)+βΔu(t-1)=f(t,u(t)),t∈[3,T]Z,where T>4,α>0,-1<β<0,f:[3,T]_(Z)×[0,∞)→R is continuous with respect to u∈[0,∞),f(t+ω,u)=f(t,u),ω∈Z^(+).The proof of the main results is based on Guo-Krasnosel'skii fixed point theorem.