Geodesic
On a class of elliptic systems in \(\mathbb R^n\)
Electronic journal of differential equations, Tome 1994 (1994) no. 7
We consider a class of variational systems in

$ \left\{ \eqalign{ - \Delta u + a(x) u \= F_u(x,u,v) \cr - \Delta v + b(x) v \= F_v(x,u,v) \,,} \right. $

where $a, b: R^N \rightarrow R$ are continuous functions which are coercive; i.e., $a(x)$ and $b(x)$ approach plus infinity as x approaches plus infinity. Under appropriate growth and regularity conditions on the nonlinearities $F_u(.)$ and $F_v(.)$, the (weak) solutions are precisely the critical points of a related functional defined on a Hilbert space of functions u, v in $H^1( R^N)$.
Classification : 35J50, 35J55
Keywords: elliptic systems, mountain-pass theorem 
@article{EJDE_1994__1994_7_a0,
     author = {Costa,  David G.},
     title = {On a class of elliptic systems in \(\mathbb {R^n\)}},
     journal = {Electronic journal of differential equations},
     year = {1994},
     volume = {1994},
     number = {7},
     zbl = {0809.35020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1994__1994_7_a0/}
}
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%A Costa,  David G.
%T On a class of elliptic systems in \(\mathbb R^n\)
%J Electronic journal of differential equations
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%F EJDE_1994__1994_7_a0
Costa,  David G. On a class of elliptic systems in \(\mathbb R^n\). Electronic journal of differential equations, Tome 1994 (1994) no. 7. http://geodesic.mathdoc.fr/item/EJDE_1994__1994_7_a0/