奇异超线性Emden-Fowler方程m-点边值问题的正解

Positive Solutions to Singular Boundary Value Problems of m-point Superlinear Emden-Fowler Equation

应用锥上不动点定理,给出了奇异非线性二阶m-点边值问题x″+a(t)xλ(t)=0,t∈(0,1)x(0)=0,x(1)=∑m-2i=1aix(ξi)存在C[0,1]正解的充分必要条件.这里ξ∈(0,1),i=1,2,…,m-2,0<ξ1<ξ2<…<ξm-2<1,ai∈R(i=1,2,…m-2),0<∑m-2i=1aiξi<1,a∈C((0,1),[0,∞)),λ∈(1,∞).

By means of the fixed point theorem on cons, a necessary and sufficient condition for the existence of C[0, 1] positive solutions is given to singular boundary value problems of a class of second order m-point superlinear differential equations {x″＋a（t）x^λ（t）=0,t∈（0,1） x（0）=0,x（1）=∑i=1^m-2aix（ξi） Where ξ∈（0,1）,is a constant 0〈ξ1〈ξ2〈…〈ξm-2〈1,ai∈R（i=1,2,…m-2）,0〈∑i=1^m-2aiξi〈1,a∈C（（0,1）,[0,∞））,λ∈（1,∞）.