一类含导数的非线性m-点边值问题的正解存在性

Existence of Positive Solutions for a Nonlinear m-point Boundary Value Problems with Derivative

通过利用Krasnosel′skii不动点定理的扩充定理,对于一类含导数的非线性二阶m-点边值问题(1.1)+(1.2)u″(t)+f(t,u(t),u′(t))=0,0<t<1(1.1)u(0)=∑m-2i=1aiu(ξi),u′(1)=∑m-2i=1biu′(ξi)(1.2)建立了至少一个正解的存在性定理,而且说明对边值条件(1.2)的几种特殊情况,也可得到类似的正解存在性定理,并对两点边值问题的存在性定理给出证明.最后给出例子对主要定理加以说明.

Abstract： By making use of an extension Krasnosel＇skii fixed point theorem in cones, it is estahlished theft existence theorem of at least one positive sohltion for a class of nonlinear second-order m-point boundary value problems with derivative （1, 1） ＋ （1, 2）,u″（t）＋f（t,u（t）,u′（t））=0,0〈t〈1 （1.1） u（0）=∑i=l^m-2aiu（ξi）,u′（1）=∑i=1^m-2biu′（ξi）（1.2） and it is illustrated to obtain similar existence theorems of positive solutions for some exceptional cases of boundary vahle condition（1.2）, and it is proofed that existence theorem of two-point boundary value problems. At last, an example is given to demonstrate the chief theorem.