Existence and multiplicity results for the fractional magnetic Schrödinger equations with critical growth

In this paper, we study the following critical fractional Schrödinger equations with the magnetic field: ε2s(−Δ)A/εsu+V(x)u=λf(|u|)u+|u|2s*−2uinRN, where ɛ and λ are positive parameters and V:RN→R and A:RN→RN are continuous electric and magnetic potentials, respectively. Under a global assumption on...

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Bibliographic Details
Published in:Journal of mathematical physics 2021-06, Vol.62 (6)
Main Authors: Guo, Ya-Hong, Sun, Hong-Rui, Cui, Na
Format: Article
Language:English
Subjects:
Mathematical analysis
Physics
Schrodinger equation
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Summary:In this paper, we study the following critical fractional Schrödinger equations with the magnetic field: ε2s(−Δ)A/εsu+V(x)u=λf(|u|)u+|u|2s*−2uinRN, where ɛ and λ are positive parameters and V:RN→R and A:RN→RN are continuous electric and magnetic potentials, respectively. Under a global assumption on the potential V, by applying the method of Nehari manifold, Ekeland’s variational principle, and Ljusternick–Schnirelmann theory, we show the existence of ground state solution and multiplicity of non-negative solutions for the above equation for all sufficiently large λ and small ɛ. In this problem, f is only continuous, which allows us to study larger classes of nonlinearities.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0041372