A Morse-Smale index theorem for indefinite elliptic systems and bifurcation

Alessandro Portaluri; Nils Waterstraat

doi:10.1016/j.jde.2014.11.010

A Morse-Smale index theorem for indefinite elliptic systems and bifurcation

Alessandro Portaluri, Nils Waterstraat

Mathematics

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

Abstract

We generalise the semi-Riemannian Morse index theorem to non-degenerate elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems, where the bifurcation parameter is introduced by shrinking the domain to a point. This extends recent results of the authors for scalar equations.

Original language	English (US)
Pages (from-to)	1715-1748
Number of pages	34
Journal	Journal of Differential Equations
Volume	258
Issue number	5
DOIs	https://doi.org/10.1016/j.jde.2014.11.010
State	Published - Mar 5 2015

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2014.11.010

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title = "A Morse-Smale index theorem for indefinite elliptic systems and bifurcation",

abstract = "We generalise the semi-Riemannian Morse index theorem to non-degenerate elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems, where the bifurcation parameter is introduced by shrinking the domain to a point. This extends recent results of the authors for scalar equations.",

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AU - Waterstraat, Nils

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AB - We generalise the semi-Riemannian Morse index theorem to non-degenerate elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems, where the bifurcation parameter is introduced by shrinking the domain to a point. This extends recent results of the authors for scalar equations.

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A Morse-Smale index theorem for indefinite elliptic systems and bifurcation

Abstract

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