Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 03, pp. 1-10.

Title: Existence and approximation of solutions of second order
       nonlinear Neumann problems

Author: Rahmat Ali Khan (Univ. of Glasgow, UK)

Abstract: 
 We study existence and approximation of solutions of some Neumann
 boundary-value problems in the presence of an upper solution
 $\beta$ and a lower solution $\alpha$ in the reversed order
 ($\alpha\geq \beta$). We use the method of quasilinearization for
 the existence and approximation of solutions.
 We also discuss quadratic convergence of the sequence of approximants.

Submitted November 6, 2004. Published January 2, 2005.
Math Subject Classifications: 34A45, 34B15.
Key Words: Neumann problems; quasilinearization;  quadratic convergence.