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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Texas State University
1999-10-01
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Online Access: | http://ejde.math.txstate.edu/Volumes/1999/40/abstr.html |
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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 |
_version_ |
1725682620197502976 |