A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions

被引：49
作者：
Cherpion, M
De Coster, C
Habets, P
机构：
[1] Univ Catholique Louvain, Inst Math Pure & Appl, B-1348 Louvain, Belgium
[2] Univ Littoral Cote Opale, Ctr Univ Mi Voix, F-62228 Calais, France
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2001年 / 123卷 / 01期
关键词：
monotone iterative method; lower and upper solutions; Neumann problem; computable approximations;
D O I：
10.1016/S0096-3003(00)00058-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper concerns the monotone approximations of solutions of boundary value problems such as -u"+f(t,u,u')=0, u'(0)=u'(1)=0. We consider linear iterative scheme in case f is Lipschitz in u' and satisfies a one-sided Lipschitz condition in u. The initial approximations are lower and upper solutions which can be ordered one way (alpha less than or equal to beta) or the other (alpha greater than or equal to beta). We also consider the periodic and the Dirichlet problems. (C) 2001 Elsevier Science Inc. All rights reserved.
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页码：75 / 91
页数：17
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