Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions

We prove the existence of nontrivial solutions to the system Δu = u, Δv = v, on a bounded set of ℝN, with nonlinear coupling at the boundary given by ∂u/∂η = Hv, ∂v/∂η = Hu. The proof is done under suitable assumptions on the Hamiltonian H, and based on a variational argument that is a generalizatio...

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Autores principales: Bonder, J.F., Pinasco, J.P., Rossi, J.D.
Formato: JOUR
Materias:
Elliptic systems
Nonlinear boundary conditions
Variational problems
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_10726691_v1999_n_p1_Bonder
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_10726691_v1999_n_p1_Bonder2023-10-03T16:02:45Z Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions Bonder, J.F. Pinasco, J.P. Rossi, J.D. Elliptic systems Nonlinear boundary conditions Variational problems We prove the existence of nontrivial solutions to the system Δu = u, Δv = v, on a bounded set of ℝN, with nonlinear coupling at the boundary given by ∂u/∂η = Hv, ∂v/∂η = Hu. 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. Fil:Pinasco, J.P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10726691_v1999_n_p1_Bonder
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Elliptic systems
Nonlinear boundary conditions
Variational problems
spellingShingle Elliptic systems
Nonlinear boundary conditions
Variational problems
Bonder, J.F.
Pinasco, J.P.
Rossi, J.D.
Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions
topic_facet Elliptic systems
Nonlinear boundary conditions
Variational problems
description We prove the existence of nontrivial solutions to the system Δu = u, Δv = v, on a bounded set of ℝN, with nonlinear coupling at the boundary given by ∂u/∂η = Hv, ∂v/∂η = Hu. 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.
format JOUR
author Bonder, J.F.
Pinasco, J.P.
Rossi, J.D.
author_facet Bonder, J.F.
Pinasco, J.P.
Rossi, J.D.
author_sort Bonder, J.F.
title Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions
title_short Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions
title_full Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions
title_fullStr Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions
title_full_unstemmed Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions
title_sort existence results for hamiltonian elliptic systems with nonlinear boundary conditions
url http://hdl.handle.net/20.500.12110/paper_10726691_v1999_n_p1_Bonder
work_keys_str_mv AT bonderjf existenceresultsforhamiltonianellipticsystemswithnonlinearboundaryconditions
AT pinascojp existenceresultsforhamiltonianellipticsystemswithnonlinearboundaryconditions
AT rossijd existenceresultsforhamiltonianellipticsystemswithnonlinearboundaryconditions
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