一类二阶边值问题解的存在性

讨论了一类椭圆问题:-u″+a(x)u=f(x,u),u(0)=u(1)=0,a∈C([0,1],R+),f∈C~1([0,1]×R~1,R~1)且对任意的x∈[0,1]有f(x,0)=0.我们首先给出了关于f的一些条件,然后运用强单调算子原理建立了此问题唯一解的存在性结果.

Existence of Solutions of a Kind of Second-Order Boundary Value Problem

In this paper,the existence of solutions are obtained for the following kind of second-order elliptic boundary value problems:-u″+a(x)u=f(x,u),u(0)=u(1)=0,a∈C([0,1],R_+),f∈C~1([0,1]×R~1,R~1),and f(x,0)=0 for all x∈[0,1].Our treatment is based on the Strongly monotone operator principle and we give some conditions that f satisfy.