Large versus bounded solutions to sublinear elliptic problems
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 67 (2019) no. 1, pp. 69-82
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $L $ be a second order elliptic operator with smooth coefficients defined on a domain $\varOmega \subset \mathbb {R}^d$ (possibly unbounded), $d\geq 3$. We study nonnegative continuous solutions $u$ to the equation $L u(x) - \varphi (x, u(x))=0$ on $\varOmega $, where $\varphi $ is in the Kato class with respect to the first variable and it grows sublinearly with respect to the second variable. Under fairly general assumptions we prove that if there is a bounded nonzero solution then there is no large solution.
Keywords:
second order elliptic operator smooth coefficients defined domain varomega subset mathbb possibly unbounded geq study nonnegative continuous solutions equation varphi varomega where varphi kato class respect first variable grows sublinearly respect second variable under fairly general assumptions prove there bounded nonzero solution there large solution
Affiliations des auteurs :
Ewa Damek 1 ; Zeineb Ghardallou 2
@article{10_4064_ba8180_12_2018,
author = {Ewa Damek and Zeineb Ghardallou},
title = {Large versus bounded solutions to sublinear elliptic problems},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
pages = {69--82},
publisher = {mathdoc},
volume = {67},
number = {1},
year = {2019},
doi = {10.4064/ba8180-12-2018},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ba8180-12-2018/}
}
TY - JOUR AU - Ewa Damek AU - Zeineb Ghardallou TI - Large versus bounded solutions to sublinear elliptic problems JO - Bulletin of the Polish Academy of Sciences. Mathematics PY - 2019 SP - 69 EP - 82 VL - 67 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/ba8180-12-2018/ DO - 10.4064/ba8180-12-2018 LA - en ID - 10_4064_ba8180_12_2018 ER -
%0 Journal Article %A Ewa Damek %A Zeineb Ghardallou %T Large versus bounded solutions to sublinear elliptic problems %J Bulletin of the Polish Academy of Sciences. Mathematics %D 2019 %P 69-82 %V 67 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/ba8180-12-2018/ %R 10.4064/ba8180-12-2018 %G en %F 10_4064_ba8180_12_2018
Ewa Damek; Zeineb Ghardallou. Large versus bounded solutions to sublinear elliptic problems. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 67 (2019) no. 1, pp. 69-82. doi: 10.4064/ba8180-12-2018
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