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

Abstract

We consider the following class of nonlinear singular differential equation subject to the Neumann boundary condition $y\text{'}\left(0\right)=y\text{'}\left(1\right)=0$. Conditions on $p\left(x\right)$ and $q\left(x\right)$ ensure that $x=0$ is 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 $(v_0\le u_0)$ or the other $(u_0\le v_0)$.