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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Texas State University
1999-10-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/1999/40/abstr.html |
| 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 $$partial u/partialeta = H_v,quad partial v/partialeta = H_u,.$$ 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. |
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| ISSN: | 1072-6691 |