Geodesic
On a class of elliptic systems in $\Bbb R^n$
Electronic Journal of Differential Equations, Tome 1994 (1994) no. 7.

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

Summary: 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 
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     author = {Costa, David G.},
     title = {On a class of elliptic systems in $\Bbb R^n$},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1994},
     number = {7},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1994__1994_7_a0/}
}
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Costa, David G. On a class of elliptic systems in $\Bbb R^n$. Electronic Journal of Differential Equations, Tome 1994 (1994) no. 7. http://geodesic.mathdoc.fr/item/EJDE_1994__1994_7_a0/