n this paper we focus our attention on the following nonlinear fractional Schrödinger equation with magnetic field ε2s(−Δ)A/ε su+V(x)u=f(|u|2)u in RN, where ε>0 is a parameter, s∈(0,1), N≥3, (−Δ)A s is the fractional magnetic Laplacian, V:RN→R and A:RN→RN are continuous potentials and f:RN→R is a subcritical nonlinearity. By applying variational methods and Ljusternick–Schnirelmann theory, we prove existence and multiplicity of solutions for ε small.

Nonlinear fractional magnetic Schrödinger equation: existence and multiplicity

D'Avenia, P.
2018-01-01

Abstract

n this paper we focus our attention on the following nonlinear fractional Schrödinger equation with magnetic field ε2s(−Δ)A/ε su+V(x)u=f(|u|2)u in RN, where ε>0 is a parameter, s∈(0,1), N≥3, (−Δ)A s is the fractional magnetic Laplacian, V:RN→R and A:RN→RN are continuous potentials and f:RN→R is a subcritical nonlinearity. By applying variational methods and Ljusternick–Schnirelmann theory, we prove existence and multiplicity of solutions for ε small.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/114304
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