一类非线性三阶边值问题正解集的全局结构

Global structure of the set of positive solutions for a class of nonlinear third-order boundary value problems

考虑一类非线性三阶常微分方程边值问题{-u(3)(t)=λf(t,u(t)),a.e.t∈[0,1],u(0)=u'(0)=0,u'(1)=αu'(η)正解集的全局结构,其中f:[0,1]×R→[0,∞)为L1-Carathéodory函数,0<η<1且1<α<1/η为常数。在f满足线性增长的条件下,运用Rabinowitz全局分歧定理得到其正解集的全局结构。

This paper considers the global structure of the set of positive solutions of nonlinear third-order ordinary differential equations boundary value problems{-u(3)(t)=λf(t,u(t)),a.e.t∈[0,1],u(0)=u'(0)=0,u'(1)=αu'(η),where f:[0,1]×R→[0,∞)is a L1-Carathéodory function,0<η<1,1<α<1/ηare given constants.When f satisfies the linear growth condition,the paper obtains the global structure of the set of positive solutions of the problem by using Rabinowitz global bifurcation theorem.