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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
