Geodesic
Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions
Electronic journal of differential equations, Tome 1999 (1999)
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__a106,
     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},
     year = {1999},
     volume = {1999},
     zbl = {0936.35064},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a106/}
}
TY  - JOUR
AU  - Fernández Bonder,  Julián
AU  - Pinasco,  Juan Pablo
AU  - Rossi,  Julio D.
TI  - Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions
JO  - Electronic journal of differential equations
PY  - 1999
VL  - 1999
UR  - http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a106/
LA  - en
ID  - EJDE_1999__1999__a106
ER  - 
%0 Journal Article
%A Fernández Bonder,  Julián
%A Pinasco,  Juan Pablo
%A Rossi,  Julio D.
%T Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions
%J Electronic journal of differential equations
%D 1999
%V 1999
%U http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a106/
%G en
%F EJDE_1999__1999__a106
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__a106/