偶数阶三点边值问题的多个对称正解

Multiple Symmetric Positive Solutions to Even Order Three point Boundary value problems

讨论了偶数阶三点边值问题:(-1)my(2m)=f(t,y),0≤t≤1,u(t)=u(1-t),αiu(2i)(0)-βiu(2i)(1)=γiu21,0≤i≤m-1.对称正解的存在性条件.借助于Leggett-Williams不动点定理,建立了该问题存在三个及任意奇数个对称正解的充分条件.

This paper discusses the existence of positive solution to the following even order boundary value problem（-1）my（2m）=f（t,y）,0≤t≤1,u（t）=u（1-t）,αiu^（2i）（0）-βiu^（2i）（1）=γiu（1/2）,0≤i≤m-1. Sufficient conditions are obtained for existence of three or arbitrary odd symmetric positive solutions of the above problem by using LeggettWilliams fixed point theorem.