Morse homology for strongly indefinite functionals on Banach spaces

L. Asselle; S. Cingolani; M. Starostka

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arXiv · 2602.20863

Morse homology for strongly indefinite functionals on Banach spaces

L. Asselle·S. Cingolani·M. Starostka

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Abstract

In this paper we lay the foundations for the Morse theoretical study of strongly indefinite functionals on Banach manifolds by developing the local theory for a specific model class that captures several key analytical features also arising in the variational formulations of geometric problems such as Dirac-harmonic maps. As a corollary, we obtain existence results of solutions to certain systems of quasilinear elliptic problems involving the $p$-area functional. Abstracting from the concrete setting, we then formulate general conditions ensuring that Morse homology is well-defined for strongly indefinite functionals on a Banach space.

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L. Asselle, S. Cingolani, M. Starostka. 2026-02-24. Morse homology for strongly indefinite functionals on Banach spaces. https://arxiv.org/abs/2602.20863

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