用Leggett-Williams不动点定理求多点边值问题的3个正解(英文)

Three Positive Solutions of Multi-point BVPs Established by Using Leggett-Williams Fixed Point Theorem

Sturm-L iouville边值问题有许多应用,并且被许多人已研究过,大多数研究的结果主要集中在至少一个正解的存在性上.研究了更一般的Sturm-L iouville多点边值问题,通过应用Leggett-W illiam s不动点定理,建立了多点边值问题至少存在3个正解的充分条件,从而推广了以前的定理,并举例说明了所得主要定理的有效性.

Sturm-Liouville boundary value problems have many applications and have been studied by many people. Most of the known results focus on the existence of at least one positive solutions. In this paper, a generalized Sturm-Liouville multi-point boundary value problem is studied. By using Leggett-Williams fixed point theorem, the sufficient conditions for at least three positive solutions of the mentioned mult-point BVPs to exist are established. Hence the present theorems are extended. An example is given to illustrate the efficiency of the main theorem.