一类三阶周期边值共振问题解的存在性

Existence of solutions for a class of third-order periodic boundary value problems at resonance

本文研究了三阶周期边值共振问题{v'''(t)=f(t,v(t)),t∈[0,T],v^(i)(0)-v^(i)(T)=0,i=0,1,2解的存在性,其中函数f:[0,T]×R→R连续且有界.当非线性项f满足适当条件时,本文发展了上下解方法并得到其解的存在性.主要结果的证明基于Lyapunov-Schmidt过程和解集连通理论.

In this paper, we consider the existence of solutions for a third-order periodic boundary value problem at resonance {v？（t）=f（t,v（t））,t∈[0,T],v^（i）（0）-v^（i）（T）=0,i=0,1,2, where f. [-0, T] R-＋ R is continuous and bounded, we develope the method of upper tions and obtain the existence of solution under suitable assumptions on f. The proof is Lyapunov-Schmidt procedure and the connectivity theory. and lower solu based upon