Fixed sign solutions of second-order difference equations with Neumann boundary conditions

被引：13

作者：

Cabada, A ^{[1
]}

Otero-Espinar, V ^{[1
]}

机构：

[1] Univ Santiago de Compostela, Fac Matemat, Dept Anal Matemat, Santiago De Compostela 15782, Galica, Spain

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2003年 / 45卷 / 6-9期

关键词：

Neumann difference equations; lower and upper solutions; monotone iterative technique; Green functions; maximum principles;

D O I：

10.1016/S0898-1221(03)00071-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 gamma and beta, we obtain optimal existence results for the case gamma less than or equal to beta and even for gamma greater than or equal to beta. To this end, we do an exhaustive study of the values of the real parameters alpha and mu, for which the associated Green's function to the linear operator L[alpha, mu]u(k) equivalent to u(k+2) - 2 alpha u(k+1) + mu uk with Neumann boundary conditions has fixed sign. (C) 2003 Elsevier Science Ltd. All rights reserved.

引用

页码：1125 / 1136

页数：12

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