一类非线性二阶常微分方程周期问题正解的存在性

Existence of positive solutions for a class of nonlinear second-order periodic problems

本文研究了非线性二阶常微分方程周期边值问题{-u″+μ2 u=λg(t)f(u),0<t<2π,u(0)=u(2π),u′(0)=u′(2π)正解的存在性,其中μ>0为常数,λ是一个正参数,g:[0,2π]→[0,∞),f:[0,α)→[0,∞)为连续函数,α>0为常数.主要结果的证明基于锥拉伸与压缩不动点定理.

In this paper, we consider the existence of positive solutions for the nonlinear second-order periodic problems. {-u″＋μ^2 u=λg（t）f（u）,0〈t〈2π, u（0）=u（2π）,u′（0）=u′（2π） where μ〉0 is a constant, λ is a positive parameter, g：[0,2π]→[0,∞）,f：[0,α）→[0,∞） are continuous functions, and a 〉 0 is a constant.The proofs of the main results are based on the fixed-point theorem of cone expansion-compression.