$T$-$p(x)$-solutions for nonlinear elliptic equations with an $L^{1}$-dual datum
Applicationes Mathematicae, Tome 39 (2012) no. 3, pp. 339-364
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We establish the existence of a $T$-$p(x)$-solution
for the $p(x)$-elliptic problem
$$
-{\rm div} (a(x,u,\nabla u))+g(x,u)=f-{\rm div} F\quad\mbox{ in } \varOmega,
$$
where $\varOmega$ is a bounded open domain of $\mathbb{R}^{N}$, $N\geq 2$ and
$a:\varOmega\times \mathbb{R}\times \mathbb{R}^{N}\rightarrow \mathbb{R}^{N}$ is
a Carathéodory function satisfying the natural growth condition and the coercivity
condition, but with only a weak monotonicity condition. The right
hand side $f$ lies in $L^1(\varOmega)$
and $F$ belongs to $\prod_{i=1}^{N}L^{p'(\cdot)} (\varOmega)$.
Keywords:
establish existence t p solution elliptic problem div nabla f div quad mbox varomega where varomega bounded domain mathbb geq varomega times mathbb times mathbb rightarrow mathbb carath odory function satisfying natural growth condition coercivity condition only weak monotonicity condition right side lies varomega belongs prod cdot varomega
Affiliations des auteurs :
El Houssine Azroul 1 ; Abdelkrim Barbara 1 ; Meryem El Lekhlifi 2 ; Mohamed Rhoudaf 3
@article{10_4064_am39_3_8,
author = {El Houssine Azroul and Abdelkrim Barbara and Meryem El Lekhlifi and Mohamed Rhoudaf},
title = {$T$-$p(x)$-solutions for nonlinear elliptic equations with an $L^{1}$-dual datum},
journal = {Applicationes Mathematicae},
pages = {339--364},
year = {2012},
volume = {39},
number = {3},
doi = {10.4064/am39-3-8},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/am39-3-8/}
}
TY - JOUR
AU - El Houssine Azroul
AU - Abdelkrim Barbara
AU - Meryem El Lekhlifi
AU - Mohamed Rhoudaf
TI - $T$-$p(x)$-solutions for nonlinear elliptic equations with an $L^{1}$-dual datum
JO - Applicationes Mathematicae
PY - 2012
SP - 339
EP - 364
VL - 39
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4064/am39-3-8/
DO - 10.4064/am39-3-8
LA - en
ID - 10_4064_am39_3_8
ER -
%0 Journal Article
%A El Houssine Azroul
%A Abdelkrim Barbara
%A Meryem El Lekhlifi
%A Mohamed Rhoudaf
%T $T$-$p(x)$-solutions for nonlinear elliptic equations with an $L^{1}$-dual datum
%J Applicationes Mathematicae
%D 2012
%P 339-364
%V 39
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4064/am39-3-8/
%R 10.4064/am39-3-8
%G en
%F 10_4064_am39_3_8
El Houssine Azroul; Abdelkrim Barbara; Meryem El Lekhlifi; Mohamed Rhoudaf. $T$-$p(x)$-solutions for nonlinear elliptic equations with an $L^{1}$-dual datum. Applicationes Mathematicae, Tome 39 (2012) no. 3, pp. 339-364. doi: 10.4064/am39-3-8
Cité par Sources :