Electron. J. Diff. Eqns.,
Vol. 1994(1994), No. 07, pp. 1-14.

### On a Class of Elliptic Systems in

David G. Costa

**Abstract:**

We consider a class of variational systems in
of the form

where
are continuous functions
which are coercive; i.e.,
and
approach plus
infinity as x approaches plus infinity. Under appropriate growth
and regularity conditions on the nonlinearities
and
, the (weak) solutions are precisely the critical points
of a related functional defined on a Hilbert space of functions
u, v in
.

By considering a class of potentials
which are
nonquadratic at infinity, 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
and
may
assume negative values, and the potential
may grow
either faster of slower than

Submitted April 21, 1994. Published September 23, 1994.

Math Subject Classification: 35J50, 35J55.

Key Words: Elliptic systems, Mountain-Pass Theorem, Nonquadratic at

Show me the
PDF file (222 KB),
TEX file, and other files for this article.

David G. Costa

Department of Mathematical sciences, University of Nevada,
Las Vegas, NV 89154, USA

Dpto. Matematica Universidade de Brasilia, 70910 Brasilia, DF Brazil

e-mail: costa@nevada.edu

Return to the EJDE home page.