Electron. J. Diff. Equ., Vol. 2012 (2012), No. 04, pp. 1-10.

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

Amit K. Verma

Monotone iterative technique is employed for studying the existence of solutions to the second-order nonlinear singular boundary value problem
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 9, 2012.
Math Subject Classifications: 34B16.
Key Words: Monotone iterative technique; lower and upper solutions; Neumann boundary conditions.

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Amit K. Verma
Department of Mathematics, BITS Pilani
Pilani - 333031, Rajasthan, India
Phone +919413789285; fax: +911596244183
email: amitkverma02@yahoo.co.in, akverma@bits-pilani.ac.in

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