一类非线性二阶三点边值问题的可解性

The solvability on a nonlinear second-order three-point boundary value problem

设f:[0,1]×R→R的连续函数.设η∈[0,1],α,β∈R且α≠1,β≠1为给定常数.在非线性项f满足某种增长条件的前提下考虑非线性二阶三点边值问题u"+f(t,u)=0,0<t<1,u (0)=αu (η),u(1)=βu(η)的可解性,建立了此问题非平凡解存在的几个充分条件.研究工具是Leray-Schauder非线性抉择.

Let f∈C([0,1]×R,R). Let η∈(0,1),α,β∈R and α≠1,β≠1 be given constant. Under certain growth condition on the nonlinearity f,it is investigated that the existence of solutions for second-order three-point boundary value problemu'+f(t,u)=0, 0<t<1, u'(0)=αu'(η),u(1)=βu(η).Several sufficient conditions for the existence of nontrivial solution are obtained.Our analysis is based on a nonlinear alternative of Leray-Schauder.