Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 04, pp. 1-10.

Title: Monotone iterative method and regular singular
       nonlinear BVP in the presence of reverse ordered upper
       and lower solutions

Author: Amit K. Verma (BITS, Pilani, Rajasthan, India)

Abstract:
 Monotone iterative technique is employed for studying the existence
 of  solutions to the second-order nonlinear singular boundary
 value problem
 $$
 -\big(p(x)y'(x)\big)'+p(x)f\big(x,y(x),p(x)y'(x)\big)=0
 $$
 for $0<x<1$ and $y'(0)=y'(1)=0$. Here $p(0)=0$ and
 $x p'(x)/p(x)$ is analytic at $x=0$. The source function
 $f(x,y,py')$ is Lipschitz in $py'$ and one sided Lipschitz in $y$.
 The initial approximations are upper solution $u_0(x)$ and lower
 solution $v_0(x)$ which can be ordered in one way
 $v_0(x)\leq u_0(x)$ or the other $u_0(x)\leq v_0(x)$.

Submitted October 19, 2011. Published January 09, 2012.
Math Subject Classifications: 34B16.
Key Words: Monotone iterative technique;  lower and upper solutions; 
           Neumann boundary conditions.