On bifurcation for semilinear elliptic Dirichlet problems and the Morse-Smale index theorem

Alessandro Portaluri; Nils Waterstraat

doi:10.1016/j.jmaa.2013.06.037

On bifurcation for semilinear elliptic Dirichlet problems and the Morse-Smale index theorem

Alessandro Portaluri, Nils Waterstraat

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study bifurcation from a branch of trivial solutions of semilinear elliptic Dirichlet boundary value problems on star-shaped domains, where the bifurcation parameter is introduced by shrinking the domain. In the proof of our main theorem we obtain in addition a special case of an index theorem due to S. Smale.

Original language	English (US)
Pages (from-to)	572-575
Number of pages	4
Journal	Journal of Mathematical Analysis and Applications
Volume	408
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2013.06.037
State	Published - Dec 15 2013

Keywords

Crossing forms
Morse index theorem
Semilinear elliptic PDE
Variational bifurcation

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2013.06.037

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title = "On bifurcation for semilinear elliptic Dirichlet problems and the Morse-Smale index theorem",

abstract = "We study bifurcation from a branch of trivial solutions of semilinear elliptic Dirichlet boundary value problems on star-shaped domains, where the bifurcation parameter is introduced by shrinking the domain. In the proof of our main theorem we obtain in addition a special case of an index theorem due to S. Smale.",

keywords = "Crossing forms, Morse index theorem, Semilinear elliptic PDE, Variational bifurcation",

author = "Alessandro Portaluri and Nils Waterstraat",

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AU - Waterstraat, Nils

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N2 - We study bifurcation from a branch of trivial solutions of semilinear elliptic Dirichlet boundary value problems on star-shaped domains, where the bifurcation parameter is introduced by shrinking the domain. In the proof of our main theorem we obtain in addition a special case of an index theorem due to S. Smale.

AB - We study bifurcation from a branch of trivial solutions of semilinear elliptic Dirichlet boundary value problems on star-shaped domains, where the bifurcation parameter is introduced by shrinking the domain. In the proof of our main theorem we obtain in addition a special case of an index theorem due to S. Smale.

KW - Crossing forms

KW - Morse index theorem

KW - Semilinear elliptic PDE

KW - Variational bifurcation

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On bifurcation for semilinear elliptic Dirichlet problems and the Morse-Smale index theorem

Abstract

Keywords

ASJC Scopus subject areas

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