On a Class of Elliptic Systems in R N
نویسنده
چکیده
We consider a class of variational systems in R N of the form where a; b : R N ! R are continuous functions which are coercive; i.e., a(x) and b(x) approach plus innnity as x approaches plus innnity. Under appropriate growth and regularity conditions on the nonlinearities Fu(:) and Fv (:), the (weak) solutions are precisely the critical points of a related functional deened on a Hilbert space of functions u; v in H 1 (R N). By considering a class of potentials F (x; u; v) which are nonquadratic at innnity, we show that a weak version of the Palais-Smale condition holds true and that a nontrivial solution can be obtained by the Generalized Mountain Pass Theorem. Our approach allows situations in which a(:) and b(:) may assume negative values, and the potential F (x; s) may grow either faster of slower than jsj 2
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