USA-Chile Workshop on Nonlinear Analysis,
Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 141-154.

Infinitely many solutions for an elliptic system with nonlinear boundary conditions

Julian Fernandez Bonder, Juan Pablo Pinasco, & Julio D. Rossi

Abstract:
In this paper we prove the existence of infinitely many nontrivial solutions of the system
$\Delta u = u$,   $\Delta v = v$,
with nonlinear coupling at the smooth boundary of a bounded domain of $\mathbb{R}^N$. The proof, under suitable assumptions on the Hamiltonian, is based on variational arguments and on the Fountain Theorem of the critical

Published January 8, 2001.
Math Subject Classifications: 35J65, 35J50, 35J55.
Key Words: Elliptic systems, nonlinear boundary conditions, variational problems.

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Julian Fernandez Bonder
Departamento de Matem\'atica, FCEyN
UBA (1428) Buenos Aires, Argentina
e-mail: jfbonder@dm.uba.ar

Juan Pablo Pinasco
Universidad de San Andres
Vito Dumas 284 (1684), Prov. Buenos Aires, Argentina
e-mail: jpinasco@udesa.edu.ar

Julio D. Rossi
Departamento de Matem\'atica, FCEyN
UBA (1428) Buenos Aires, Argentina
e-mail: jrossi@dm.uba.ar

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