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doi:10.1016/S0898-1221(03)00071-3 
Copyright © 2003 Published by Elsevier Science Ltd.
Fixed sign solutions of second-order difference equations with Neumann boundary conditions*1
A. Cabada
and V. Otero-Espinar
Available online 14 October 2003.
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Abstract
In this paper, we study the existence of solution of the nonlinear second-order difference problem with Neumann boundary conditions. Assuming the existence of a pair of ordered lower and upper solutions γ and β, we obtain optimal existence results for the case γ ≤ β and even for γ ≥ β.
To this end, we do an exhaustive study of the values of the real parameters α and μ, for which the associated Green's function to the linear operator L[α,μ] uκ ≡ uκ+2 − 2 α uκ+1 + μ uκ with Neumann boundary conditions has fixed sign.
Author Keywords: Neumann difference equations; Lower and upper solutions; Monotone iterative technique; Green functions; Maximum principles
