Positive and nodal limiting profiles for a semilinear elliptic equation with a shrinking region of attraction
Autor: | Clapp, Mónica, Hernández-Santamaría, Víctor, Saldaña, Alberto |
---|---|
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 |
Externí odkaz: |