关键词: 多点边值问题, 正解, Schauder不动点定理

Abstract:

Let a∈C［0,1］, b∈C(［0,1］,(-∞, 0)).Let \-1(t) be the unique positive solution  of the linear problemu″+ a(t)u′+b(t)u=0 ,\=u′(0)=0, u(1)=1 .The author studies the existence of positive solutions for the nonhomogeneous mpoint boundary value problemu″+ a(t)u′+b(t)u+h(t)f(u)=0, \=u′(0)=0, u(1)-∑[DD(]m-2[]i=1[DD)]α\-i u(ξ\-i)=d,where d is a parameter, ξ\-i∈(0,1) and α\-i∈(0,∞)  are given constants satisfying∑[DD(]m-2[]i=1[DD)]α\-i\-1(ξ\-i) <1,i∈{1,\:,m-2}.Under suitable conditions, the author shows that there exists a positive number d\+* such that the problem has at least one positive solution for 0d\+*.

Key words: Multipoint boundary value problems, Positive solutions, Schauder fixed point theorem.