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 / Ambrosio, V.; D'Avenia, P.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 264:(2018), pp. 3336-3368. [10.1016/j.jde.2017.11.021]
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.| File | Dimensione | Formato | |
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