Nonlinear Singular BVP of Limit Circle Type and the Presence of Reverse-Ordered Upper and Lower Solutions

摘要

We consider the following class of nonlinear singular differential equation-(p(x)y′(x))′+q(x)f(x,y(x),p(x)y′(x))=0,  0<x<1subject to the Neumann boundary conditiony′(0)=y′(1)=0. Conditions onp(x)andq(x)ensure thatx=0is a singular point of limit circle type. A simple approximation scheme which is iterative in nature is considered. The initial iterates are upper and lower solutions which can be ordered in one way(v0≤u0)or the other(u0≤v0).