We describe a constructive method which yields two monotone sequences that converge uniformly to extremal solutions to the periodic boundary value problem u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) in the presence of a lower solution α(t) and an upper solution β(t) with β(t) ≤ α(t).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-3-6,
author = {Daqing Jiang and Lingbin Kong},
title = {A monotone method for constructing extremal solutions to second order periodic boundary value problems},
journal = {Annales Polonici Mathematici},
volume = {77},
year = {2001},
pages = {279-286},
zbl = {0982.34012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-3-6}
}
Daqing Jiang; Lingbin Kong. A monotone method for constructing extremal solutions to second order periodic boundary value problems. Annales Polonici Mathematici, Tome 77 (2001) pp. 279-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-3-6/