Geodesic
Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions
Electronic Journal of Differential Equations, Tome 1999 (1999).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We prove the existence of nontrivial solutions to the system $$ \Delta u = u, \quad \Delta v = v, $$ on a bounded set of $R^{N}$, 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.
Classification : 35J65, 35J20, 35J55
Keywords: elliptic systems, nonlinear boundary conditions 
@article{EJDE_1999__1999__a8,
     author = {Fern\'andez Bonder, Juli\'an and Pinasco, Juan Pablo and Rossi, Julio D.},
     title = {Existence results for {Hamiltonian} elliptic systems with nonlinear boundary conditions},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1999},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a8/}
}
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AU  - Rossi, Julio D.
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%A Rossi, Julio D.
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%J Electronic Journal of Differential Equations
%D 1999
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%F EJDE_1999__1999__a8
Fernández Bonder, Julián; Pinasco, Juan Pablo; Rossi, Julio D. Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions. Electronic Journal of Differential Equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a8/