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

Authors
Cherpion, M De Coster, C Habets, P
Citation
M. Cherpion et al., A constructive monotone iterative method for second-order BVP in the presence of lower and upper solutions, APPL MATH C, 123(1), 2001, pp. 75-91
Citations number
17
Categorie Soggetti
Engineering Mathematics
Journal title
APPLIED MATHEMATICS AND COMPUTATION
ISSN journal
00963003 → ACNP
Volume
123
Issue
1
Year of publication
2001
Pages
75 - 91
Database
ISI
SICI code
0096-3003(20010910)123:1<75:ACMIMF>2.0.ZU;2-G
Abstract
This paper concerns the monotone approximations of solutions of boundary va lue 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 satisf ies a one-sided Lipschitz condition in u. The initial approximations are lo wer and upper solutions which can be ordered one way (alpha less than or eq ual to beta) or the other (alpha greater than or equal to beta). We also co nsider the periodic and the Dirichlet problems. (C) 2001 Elsevier Science I nc. All rights reserved.