Electron. J. Diff. Eqns., Vol. 1999(1999), No. 40, pp. 1-15.

Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions

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

Abstract:
We prove the existence of nontrivial solutions to the system
$$ \Delta u  =  u, \quad \Delta v  =  v, $$
on a bounded set of RN, with nonlinear coupling at the boundary given by
$$\partial u/\partial\eta = H_v,\quad \partial v/\partial\eta = H_u\,.$$
The proof is done under suitable assumptions on the Hamiltonian H, and based on a variational argument that is a generalization of the mountain pass theorem. Under further assumptions on the Hamiltonian, we prove the existence of positive solutions.

Submitted May 30, 1999. Published October 7, 1999.
Math Subject Classifications: 35J65, 35J20, 35J55
Key Words: elliptic systems, nonlinear boundary conditions, variational problems

Show me the PDF file (166K), TEX file, and other files for this article.


Julian Fernandez Bonder
Departamento de Matematica, 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 Matematica, FCEyN
UBA (1428) Buenos Aires, Argentina.
e-mail: jrossi@dm.uba.ar


Return to the EJDE web page