Variational methods for scaled functionals with applications to the Schrödinger-Poisson-Slater equation
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912147073662976 |
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| author | Mercuri, Carlo Perera, Kanishka |
| author_facet | Mercuri, Carlo Perera, Kanishka |
| contents | We develop novel variational methods for solving scaled equations that do not have the mountain pass geometry, classical linking geometry based on linear subspaces, or $\mathbb Z_2$ symmetry, and therefore cannot be solved using classical variational arguments. Our contributions here include new critical group estimates for scaled functionals, nonlinear saddle point and linking geometries based on scaling, a notion of local linking based on scaling, and scaling-based multiplicity results for symmetric functionals. We develop these methods in an abstract setting involving scaled operators and scaled eigenvalue problems. Applications to subcritical and critical Schrödinger-Poisson-Slater equations are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_15887 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Variational methods for scaled functionals with applications to the Schrödinger-Poisson-Slater equation Mercuri, Carlo Perera, Kanishka Analysis of PDEs 58E05 (Primary). Secondary: 47J30, 35Q55, 35B06, 35J20 We develop novel variational methods for solving scaled equations that do not have the mountain pass geometry, classical linking geometry based on linear subspaces, or $\mathbb Z_2$ symmetry, and therefore cannot be solved using classical variational arguments. Our contributions here include new critical group estimates for scaled functionals, nonlinear saddle point and linking geometries based on scaling, a notion of local linking based on scaling, and scaling-based multiplicity results for symmetric functionals. We develop these methods in an abstract setting involving scaled operators and scaled eigenvalue problems. Applications to subcritical and critical Schrödinger-Poisson-Slater equations are given. |
| title | Variational methods for scaled functionals with applications to the Schrödinger-Poisson-Slater equation |
| topic | Analysis of PDEs 58E05 (Primary). Secondary: 47J30, 35Q55, 35B06, 35J20 |
| url | https://arxiv.org/abs/2411.15887 |