The existence of a positive radial solution for a sublinear elliptic boundary value problem in an exterior domain is proved, by the use of a cone compression fixed point theorem. The existence of a nonradial, positive solution for the corresponding nonradial problem is obtained by the sub- and supersolution method, under an additional monotonicity assumption.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm92-1-12,
author = {Bogdan Przeradzki and Robert Sta\'nczy},
title = {Positive solutions for sublinear elliptic equations},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {141-151},
zbl = {0992.35037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm92-1-12}
}
Bogdan Przeradzki; Robert Stańczy. Positive solutions for sublinear elliptic equations. Colloquium Mathematicae, Tome 91 (2002) pp. 141-151. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm92-1-12/