一类含参的二阶m点边值问题正解的存在性

Existence of Positive Solution for a Parameter-Containing Second-Order m-Point Boundary Value Problem

运用不动点指数理论考虑了二阶m-点边值问题u″(t)+λu(t)+f(t,u(t))=0t∈(0,1)u(0)=0u(1)=∑m-2i=1aiu(ξi)在f满足次线性或超线性条件下正解的存在性,其中λ∈[0,+∞),ai∈[0,+∞)且∑m-2i=1ai<1,ξi∈(0,1)(i=1,2,…,m-2),0<ξ1<ξ2<…<ξm-2<1,并得到了正解的一个存在性结果.

The second-order m-point boundary value problemu″（t）＋λu（t）＋f（t,u（t））=0t∈（0,1）u（0）=0u（1）=∑m-2i=1aiu（ξi）is considered under the sublinearity or superlinearity of the function f,where λ≥0,ai∈[0,＋∞） with ∑m-2i=1ai1,ξi∈（0,1）（i=1,2,…,m-2）,0ξ1ξ2…ξm-21. The existence of positive solutions is obtained by means of the fixed-point index theory.