Morse homology for strongly indefinite functionals on Banach spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912936800288768 |
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| author | Asselle, L. Cingolani, S. Starostka, M. |
| author_facet | Asselle, L. Cingolani, S. Starostka, M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20863 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Morse homology for strongly indefinite functionals on Banach spaces Asselle, L. Cingolani, S. Starostka, M. Analysis of PDEs 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. |
| title | Morse homology for strongly indefinite functionals on Banach spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2602.20863 |