We investigate the solvability of the quasilinear Neumann problem (1.1) with sub- and supercritical exponents in an unbounded domain Ω. Under some integrability conditions on the coefficients we establish embedding theorems of weighted Sobolev spaces into weighted Lebesgue spaces. This is used to obtain solutions through a global minimization of a variational functional.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-3-3,
author = {J. Chabrowski},
title = {Indefinite Quasilinear Neumann Problem on Unbounded Domains},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {54},
year = {2006},
pages = {207-217},
zbl = {1200.35141},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-3-3}
}
J. Chabrowski. Indefinite Quasilinear Neumann Problem on Unbounded Domains. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 54 (2006) pp. 207-217. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba54-3-3/