On the number and Indices of equilibria in a space-dependent bistable equation
We study a singular perturbation problem of a piecewise autonomous bistable equation. We give sufficient conditions both for the boundedness and the unboundedness of the number and Morse index of its equilibrium solutions as the perturbation parameter approaches zero. For the bounded case, we provid...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 1999 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/1210 |
| Acceso en línea: | https://hdl.handle.net/2117/1210 |
| Access Level: | acceso abierto |
| Palabra clave: | Differentiable dynamical systems Partial differential equations Parabolic partial differential equations space-dependent bistable equation Sistemes dinàmics diferenciables Equacions en derivades parcials Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems Classificació AMS::37 Dynamical systems and ergodic theory::37L Infinite-dimensional dissipative dynamical systems |
| Sumario: | We study a singular perturbation problem of a piecewise autonomous bistable equation. We give sufficient conditions both for the boundedness and the unboundedness of the number and Morse index of its equilibrium solutions as the perturbation parameter approaches zero. For the bounded case, we provide the number of equilibria as a function of the number of discontinuities of the reaction term. |
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