Geodesic
Existence of weak solutions for nonlinear elliptic systems on $\Bbb{R}^N$
Electronic Journal of Differential Equations, Tome 2006 (2006).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper, we consider the nonlinear elliptic system $$\displaylines{ -\Delta_pu=a(x)|u|^{p-2}u-b(x)|u|^\alpha|v|^\beta v+f,\cr -\Delta_qv=-c(x)|u|^\alpha |v|^\beta u + d(x) |v|^{q-2}v +g ,\cr \lim_{|x|\to\infty}u=\lim_{|x|\to\infty}v=0\quad u,v>0 }$$ on a bounded and unbounded domains of $\mathbb{R}^N$, where $\Delta_p$ denotes the p-Laplacian. The existence of weak solutions for these systems is proved using the theory of monotone operators
Classification : 35B45, 35J55
Keywords: weak solutions, nonlinear elliptic systems, p-Laplacian, monotone operators 
@article{EJDE_2006__2006__a45,
     author = {El-Zahrani, Eada A. and Serag, Hassan M.},
     title = {Existence of weak solutions for nonlinear elliptic systems on $\Bbb{R}^N$},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2006},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a45/}
}
TY  - JOUR
AU  - El-Zahrani, Eada A.
AU  - Serag, Hassan M.
TI  - Existence of weak solutions for nonlinear elliptic systems on $\Bbb{R}^N$
JO  - Electronic Journal of Differential Equations
PY  - 2006
VL  - 2006
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a45/
LA  - en
ID  - EJDE_2006__2006__a45
ER  - 
%0 Journal Article
%A El-Zahrani, Eada A.
%A Serag, Hassan M.
%T Existence of weak solutions for nonlinear elliptic systems on $\Bbb{R}^N$
%J Electronic Journal of Differential Equations
%D 2006
%V 2006
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a45/
%G en
%F EJDE_2006__2006__a45
El-Zahrani, Eada A.; Serag, Hassan M. Existence of weak solutions for nonlinear elliptic systems on $\Bbb{R}^N$. Electronic Journal of Differential Equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a45/