Electron. J. Diff. Eqns., Vol. 2005(2005), No. 03, pp. 1-10.

Existence and approximation of solutions of second order nonlinear Neumann problems

Rahmat Ali Khan

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.

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Rahmat Ali Khan
Department of Mathematics, University of Glasgow
Glasgow G12 8QW, UK
email: rak@maths.gla.ac.uk

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