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Fractional NLS equations with magnetic field, critical frequency and critical growth

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Abstract

The paper is devoted to the study of singularly perturbed fractional Schrödinger equations involving critical frequency and critical growth in the presence of a magnetic field. By using variational methods, we obtain the existence of mountain pass solutions \(u_{\varepsilon }\) which tend to the trivial solution as \(\varepsilon \rightarrow 0\). Moreover, we get infinitely many solutions and sign-changing solutions for the problem in absence of magnetic effects under some extra assumptions.

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Authors and Affiliations

  1. Department of Mathematics, Heilongjiang Institute of Technology, Harbin, 150050, People’s Republic of China

    Zhang Binlin

  2. Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via dei Musei 41, 25121, Brescia, Italy

    Marco Squassina

  3. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Zhang Xia

Authors
  1. Zhang Binlin
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  2. Marco Squassina
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  3. Zhang Xia
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Corresponding author

Correspondence to Marco Squassina.

Additional information

The second author is member of Gruppo Nazionale per l’Analisi Ma-te-ma-ti-ca, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). Zhang Binlin was supported by the Natural Science Foundation of Hei-longjiang Province of China (No. A201306), the Research Foundation of Hei-longjiang Educational Committee (No. 12541667) and the Doctoral Research Foundation of Heilongjiang Institute of Technology (No. 2013BJ15). Zhang Xia was supported by the National Science Foundation of China (No. 11601103, No. 11671111).

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Binlin, Z., Squassina, M. & Xia, Z. Fractional NLS equations with magnetic field, critical frequency and critical growth. manuscripta math. 155, 115–140 (2018). https://doi.org/10.1007/s00229-017-0937-4

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  • DOI: https://doi.org/10.1007/s00229-017-0937-4

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