Geodesic
Multiplicity of positive solutions for a gradient system with an exponential nonlinearity
Electronic journal of differential equations, Tome 2012 (2012)
In this article, we consider the problem

$\displaylines{ -\Delta u = \lambda u^{q} + f_1(u,v) \quad \hbox{in } \Omega\cr -\Delta v = \lambda v^{q} + f_{2} (u,v) \quad \hbox{in } \Omega\cr u, v > 0 \quad \hbox{in } \Omega \cr u = v = 0 \quad \hbox{on } \partial\Omega, }$

where $\Omega$ is a bounded domain in $\mathbb{R}^{2}, 0$, and $\lambda>0$. We show that there exists a real number $\Lambda$ such that the above problem admits at least two solutions for $\lambda\in(0,\Lambda)$, and no solution for $\lambda>\Lambda$.
Classification : 35J50, 35J57, 35J60
Keywords: gradient system, exponential nonlinearity, multiplicity 
@article{EJDE_2012__2012__a3,
     author = {Megrez,  Nasreddine and Sreenadh,  K. and Khaldi,  Brahim},
     title = {Multiplicity of positive solutions for a gradient system with an exponential nonlinearity},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1291.35061},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a3/}
}
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AU  - Sreenadh,  K.
AU  - Khaldi,  Brahim
TI  - Multiplicity of positive solutions for a gradient system with an exponential nonlinearity
JO  - Electronic journal of differential equations
PY  - 2012
VL  - 2012
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%J Electronic journal of differential equations
%D 2012
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%U http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a3/
%G en
%F EJDE_2012__2012__a3
Megrez,  Nasreddine; Sreenadh,  K.; Khaldi,  Brahim. Multiplicity of positive solutions for a gradient system with an exponential nonlinearity. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a3/