Electronic Journal of Differential Equations,
Conference 06 (2001), pp. 141-154.

Title: Infinitely many solutions for an elliptic system with nonlinear
  boundary conditions.

Authors: Julian Fernandez Bonder (FCEyN UBA, Buenos Aires, Argentina) 
  Juan Pablo Pinasco (Univ. de San Andres, Buenos Aires, Argentina) 
  Julio D. Rossi (FCEyN UBA, Buenos Aires, Argentina)
 
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 
  point theory. 

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