The purpose of this paper is to study the periodic boundary value problem -u''(t) = f(t,u(t),u'(t)), u(0) = u(2π), u'(0) = u'(2π) when f satisfies the Carathéodory conditions. We show that a generalized upper and lower solution method is still valid, and develop a monotone iterative technique for finding minimal and maximal solutions.
@article{bwmeta1.element.bwnjournal-article-apmv58z3p221bwm,
author = {Ming-Xing Wang and Alberto Cabada and Juan J. Nieto},
title = {Monotone method for nonlinear second order periodic boundary value problems with Carath\'eodory functions},
journal = {Annales Polonici Mathematici},
volume = {58},
year = {1993},
pages = {221-235},
zbl = {0789.34027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv58z3p221bwm}
}
Ming-Xing Wang; Alberto Cabada; Juan J. Nieto. Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions. Annales Polonici Mathematici, Tome 58 (1993) pp. 221-235. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv58z3p221bwm/
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