Positive and nodal limiting profiles for a semilinear elliptic equation with a shrinking region of attraction
| Autor: | Clapp, Mónica, Hernández-Santamaría, Víctor, Saldaña, Alberto |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the existence and concentration of positive and nodal solutions to a Schr\"odinger equation in the presence of a shrinking self-focusing core of arbitrary shape. Via a suitable rescaling, the concentration gives rise to a limiting profile that solves a nonautonomous elliptic semilinear equation with a sharp sign change in the nonlinearity. We characterize the (radial or foliated Schwarz) symmetries and the (polynomial) decay of the least-energy positive and nodal limiting profiles. Comment: Revised version |
| Databáze: | arXiv |
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