Julian Fernandez Bonder, Juan Pablo Pinasco, & Julio D. Rossi
We prove the existence of nontrivial solutions to the system
on a bounded set of RN, with nonlinear coupling at the boundary given by
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
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Juan Pablo Pinasco
Universidad de San Andres
Vito Dumas 284 (1684), Prov. Buenos Aires, Argentina.
Julio D. Rossi
Departamento de Matematica, FCEyN
UBA (1428) Buenos Aires, Argentina.