一类非线性三阶边值问题正解集的全局结构

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。

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

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/η are 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.