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On the number and Indices of equilibria in a space-dependent bistable equation
Salazar, Domingo; Solà-Morales Rubió, Joan de
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
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.
2012-05-10
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
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