非线性n阶m点边值问题正解的存在性

New Results of Positive Solutions for a Nonlinear nth-order m-point Boundary Value Problem

获得非线性n阶m点边值问题{u^((n))(t)+a(t)f(u)=0,t∈(0,1),u(0)=0,u'(0)=…=u^((n-2))(0)=0,u(1)=m-2∑i=1kiu(ξi)正解的存在性,其中,n≥2,k_(i)>0(i=1,2,…,m-2),0<ξ_(1)<ξ_(2)<…<ξ_(n-2)<1,借助Leray-Schauder原理得到正解的存在性的条件,这个条件弱化超线性条件和次线性条件.

In this paper,we investigate the existence of positive solutions for a nonlinear nth-order m-point boundary value problems{u^((n))(t)+a(t)f(u)=0,t∈(0,1),u(0)=0,u'(0)=…=u^((n-2))(0)=0,u(1)=m-2∑i=1kiu(ξi)where n≥2,k_(i)>0(i=1,2,…m-2),0<ξ_(1)<ξ_(2)<…ξ_(n-2)<1,by using the Leray-Schauder fixed point theorem.Some sufficient conditions for the existence of positive solutions are obtained,which weakens the superlinear condition and the sublinear condition.