Geodesic
Existence of weak solutions for a nonuniformly elliptic nonlinear system in \(\mathbb R^N\)
Electronic journal of differential equations, Tome 2008 (2008)
We study the nonuniformly elliptic, nonlinear system

$\displaylines{ - \hbox{div}(h_1(x)\nabla u)+ a(x)u = f(x,u,v) \quad {in } \mathbb{R}^N,\cr - \hbox{div}(h_2(x)\nabla v)+ b(x)v = g(x,u,v) \quad {in } \mathbb{R}^N. }$

Under growth and regularity conditions on the nonlinearities f and g, we obtain weak solutions in a subspace of the Sobolev space $H^1(\mathbb{R}^N, \mathbb{R}^2)$ by applying a variant of the Mountain Pass Theorem.
Classification : 35J65, 35J20
Keywords: nonuniformly elliptic, nonlinear systems, mountain pass theorem, weakly continuously differentiable functional 
@article{EJDE_2008__2008__a89,
     author = {Chung,  Nguyen Thanh},
     title = {Existence of weak solutions for a nonuniformly elliptic nonlinear system in \(\mathbb {R^N\)}},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1177.35092},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a89/}
}
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%J Electronic journal of differential equations
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Chung,  Nguyen Thanh. Existence of weak solutions for a nonuniformly elliptic nonlinear system in \(\mathbb R^N\). Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a89/