偶数阶Sturm-Liouville边值问题的多个正解

Multiple Positive Solutions for Even Order Sturm-Liouville Boundary Value Problems

该文讨论了偶数阶边值问题(-1)~m y^(2m)=f(t,y),0≤t≤1,α_(i+1y)^(2i)(0)-β_(i+1y)^(2i+1)(0)=0,γ_(i+1y)^(2i)(1)+δ_(i+1y)^(2i+1)(1)=0,0≤i≤m-1正解的存在性．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正解的充分条件．

In this paper the authors discuss the existence of positive solution to the following even order boundary value problem （-1）^my^（2m）=f（t,y）,0≤t≤1,αi＋1y^（2i）（0）-βi＋1y^（2i＋1）（0）=0,γi＋1y^（2i）（1）＋δi＋1y^（2i＋1）（1）=0,0≤i≤m-1.Sufficient conditions are obtained for existence of three or arbitrary odd positive solutions of the above problem by using Leggett-Williams fixed point theorem.