Variational methods for scaled functionals with applications to the Schr\'{o}dinger-Poisson-Slater equation
| Autor: | Mercuri, Carlo, Perera, Kanishka |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 Schr\"{o}dinger-Poisson-Slater equations are given. Comment: 75 pages (in this second version some supercritical nonlinearities are also considered) |
| Databáze: | arXiv |
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