In this paper, we study a nonlinear Neumann problem. Assuming the existence of an upper and a lower solution, we prove the existence of a least and a greatest solution between them. Our approach uses the theory of operators of monotone type together with truncation and penalization techniques.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1024,
author = {Antonella Fiacca and Raffaella Servadei},
title = {Extremal solutions for nonlinear neumann problems},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {21},
year = {2001},
pages = {191-206},
zbl = {1013.35035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1024}
}
Antonella Fiacca; Raffaella Servadei. Extremal solutions for nonlinear neumann problems. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 21 (2001) pp. 191-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1024/
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