We study the following fractional Schrödinger equation with discontinuous nonlinearity: [Formula presented], where [Formula presented], H is the Heaviside function, (−∆)s is the fractional Laplacian operator, [Formula presented] is a continuous potential satisfying del Pino-Felmer type assumptions and [Formula presented]is a superlinear continuous nonlinearity with subcritical growth at infinity. By using a penalization method and nonsmooth analysis, we investigate the existence and concentration of solutions for the above problem.
CONCENTRATION PHENOMENON FOR A FRACTIONAL SCHRÖDINGER EQUATION WITH DISCONTINUOUS NONLINEARITY / Ambrosio, V.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 16:11(2023), pp. 2919-2944. [10.3934/DCDSS.2023074]
CONCENTRATION PHENOMENON FOR A FRACTIONAL SCHRÖDINGER EQUATION WITH DISCONTINUOUS NONLINEARITY
Ambrosio V.
2023-01-01
Abstract
We study the following fractional Schrödinger equation with discontinuous nonlinearity: [Formula presented], where [Formula presented], H is the Heaviside function, (−∆)s is the fractional Laplacian operator, [Formula presented] is a continuous potential satisfying del Pino-Felmer type assumptions and [Formula presented]is a superlinear continuous nonlinearity with subcritical growth at infinity. By using a penalization method and nonsmooth analysis, we investigate the existence and concentration of solutions for the above problem.| File | Dimensione | Formato | |
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Descrizione: This article has been published in a revised form in Discrete and Continuous Dynamical Systems - Series S 10.3934/DCDSS.2023074.This version is free to download for private research and study only. Not for redistribution, re-sale or use in derivative works
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