一类非线性三阶差分方程正周期解的存在性和多解性

考虑一类非线性三阶差分方程Δ³u(t-3)+αΔ²u(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。

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

This paper considers the existence and multiplicity of positive periodic solutions for a class of nonlinear third-order difference equationΔ³u(t-3)+αΔ²u(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.