Existence and approximation of solutions of second order nonlinear Neumann problems

Abstract

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

Keywords

• Neumann problems
• quasilinearization
• quadratic convergence.