非线性奇异边值问题解的存在性

Existence of Solutions for nonlinear Singular Boundary Value Problems

研究了奇异微分边值问题x″ +f(t ,x) =0 , t∈ (0 ,1)x(0 ) =x(1) =0解的存在性 .证明了在f(t,x)关于x不增的情况下 ,其非负解存在的充要条件是存在非负下解 .同时考虑了非线性边值条件下解的存在性 .

The question considered is that the existence of solutions for singular differential boundary value problem x″+f(t,x)=0,t∈(0,1) x(0)=x(1)=0 It is obtained that the nonnegtive solution exsists if and only if its nonnegtive lower solution exists. At the same time the singular equation satisfying the nonlinear boundary value condition is also considered.