Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions

Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions

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 $$partial u/partialeta = H_v,quad partial v/partialeta = H_u,.$$ The proof is done under suitable assumptions on the Hamiltoni...

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Main Authors: Julian Fernandez Bonder, Juan Pablo Pinasco, Julio D. Rossi
Format: Article
Language:English
Published: Texas State University 1999-10-01
Series:Electronic Journal of Differential Equations
Subjects:
elliptic systems
nonlinear boundary conditions
variational problems
Online Access:http://ejde.math.txstate.edu/Volumes/1999/40/abstr.html
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spelling doaj-dc16ec34c09a41fdb709e42cf00d2c7e2020-11-24T22:47:11ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911999-10-01199940115Existence results for Hamiltonian elliptic systems with nonlinear boundary conditionsJulian Fernandez BonderJuan Pablo PinascoJulio D. RossiWe 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 $$partial u/partialeta = H_v,quad partial v/partialeta = H_u,.$$ 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. http://ejde.math.txstate.edu/Volumes/1999/40/abstr.htmlelliptic systemsnonlinear boundary conditionsvariational problems
collection DOAJ
language English
format Article
sources DOAJ
author Julian Fernandez Bonder
Juan Pablo Pinasco
Julio D. Rossi
spellingShingle Julian Fernandez Bonder
Juan Pablo Pinasco
Julio D. Rossi
Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions
Electronic Journal of Differential Equations
elliptic systems
nonlinear boundary conditions
variational problems
author_facet Julian Fernandez Bonder
Juan Pablo Pinasco
Julio D. Rossi
author_sort Julian Fernandez Bonder
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
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 1999-10-01
description 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 $$partial u/partialeta = H_v,quad partial v/partialeta = H_u,.$$ 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.
topic elliptic systems
nonlinear boundary conditions
variational problems
url http://ejde.math.txstate.edu/Volumes/1999/40/abstr.html
work_keys_str_mv AT julianfernandezbonder existenceresultsforhamiltonianellipticsystemswithnonlinearboundaryconditions
AT juanpablopinasco existenceresultsforhamiltonianellipticsystemswithnonlinearboundaryconditions
AT juliodrossi existenceresultsforhamiltonianellipticsystemswithnonlinearboundaryconditions
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