非线性二阶周期边值问题正解的全局结构

Global structure of positive solutions for a nonlinear second-order periodic boundary value problem

本文获得了二阶周期边值问题{u″(t)-k2u+λa(t)f(u)=0,t∈[0,2π],u(0)=u(2π),u′(0)=u′(2π)正解的全局结构,其中k>0为常数,λ是正参数,a∈C([0,2π],[0,∞))且在[0,2π]的任何子区间内a(t)≠0,f∈C([0,∞),[0,∞)).主要结果的证明基于Rabinowitz全局分歧理论和逼近方法.

In this paper, we study the global structure of positive solutions for second-order periodic boundary value problem {u″（t）-k2u＋λa（t）f（u）=0,t∈[0,2π],u（0）=u（2π）,u′（0）=u′（2π）,where k〉0 is a constant, ~, is positive parameter,a∈C（[0,2π],[0,∞））and a（t）≠0 on any subinterval of （[0,2π],f∈C（[0,∞）,[0,∞））.The proof of the main results is based on Rabinowitz global bifurca-tion theorems and approximation approach.