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arXiv · 1408.1419

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

Alessandro Portaluri·Nils Waterstraat
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Abstract

We generalise the semi-Riemannian Morse index theorem to 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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Alessandro Portaluri, Nils Waterstraat. 2014-08-06. A Morse-Smale index theorem for indefinite elliptic systems and bifurcation. https://arxiv.org/abs/1408.1419

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