一类奇异半正二阶两点边值问题的正解的存在性与多解性

Existence and Multiplicity of Positive Solutions to a Singular Semipositone Second-Order Two-Point Boundary Value Problem

考察了二阶常微分方程u″(t)+f(t,u(t))+h(t)=0,a.e.t∈[0,1]在Sturm-Liouville边值条件下的正解,其中f(t,u)是非负弱Caratheodory函数并且允许h(t)■0.利用锥拉伸与锥压缩型的Krasnoselskii不动点定理,建立了有限或无穷多个正解的存在性.、

The positive solutions are considered for the second-order ordinary differential equation u＂（t）＋f（t,u（t））＋h（t）=0,a.e.t∈[0,1]with Sturm-Liouville boundary condition.Here,f（t,u） is a nonnegative weak Caratheodoly function,and h（t）■ 0 is allowed.By applying Krasnosel＇skii fixed point theorem of cone expansion-compression type,the existence of finitely or infinitely many positive solutions is established.