二阶多点边值问题三个正解的存在性

Existence of Triple Positive Solutions for Second Order Multi-point Boundary Value Problem

利用一个新的不动点定理,得到了二阶非线性n-点边值问题:u″(t)+f(t,u(t))=0,t∈(0,1)u′(0)=∑n-2i=1biu′(ξi),u(1)=∑ki=1aiu(ξi)-∑n-2i=k+1aiu(ξi)至少存在三个正解的一个充分条件,其中0<ξ1<ξ2<…<ξn-2<1,ai,bi∈[0,∞)且满足0<∑ki=1ai-∑n-2i=k+1ai<1,∑n-2i=1bi<1。

Based on new fixed point theorem, a sufficient condition of at least triple positive solutions for second order nonlinear n-point boundary value problems is obtained.u＂（t）＋f（t,u（t））=0,t∈（0,1）,u＇（0）=∑i=1n-1biu＇（ξi）,u（1）=∑i=1kaiu（ξi）-∑i=k＋1n-2aiu（ξi）,where 0〈ξ1〈ξ2〈…〈ξ0-2〈1,Ai,bi∈[0,∞）and satisfying 0〈∑i-1kai-∑i=k＋1n-2ai〈1,∑i=1n-2bi〈1.