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Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials

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  • Additional Information
    • Publication Information:
      Hindawi Limited, 2019.
    • Publication Date:
      2019
    • Collection:
      LCC:Engineering (General). Civil engineering (General)
      LCC:Mathematics
    • Abstract:
      In this study, we consider the following sublinear Schrödinger equations −Δu+Vxu=fx,u,for x∈ℝN,ux⟶0,asu⟶∞, where fx,u satisfies some sublinear growth conditions with respect to u and is not required to be integrable with respect to x. Moreover, V is assumed to be coercive to guarantee the compactness of the embedding from working space to LpℝN for all p∈1,2∗. We show that the abovementioned problem admits at least one solution by using the linking theorem, and there are infinitely many solutions when fx,u is odd in u by using the variant fountain theorem.
    • File Description:
      electronic resource
    • ISSN:
      1024-123X
      1563-5147
    • Relation:
      https://doaj.org/toc/1024-123X; https://doaj.org/toc/1563-5147
    • Accession Number:
      10.1155/2019/9291534
    • Rights:
      Journal Licence: CC BY
    • Accession Number:
      edsdoj.2be5b25425644e4bb2b139181ca511fc
  • Citations
    • ABNT:
      DONG-LUN WU. Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials. Mathematical Problems in Engineering, [s. l.], v. 2019, 2019. DOI 10.1155/2019/9291534. Disponível em: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsdoj&AN=edsdoj.2be5b25425644e4bb2b139181ca511fc&custid=s8280428. Acesso em: 28 set. 2020.
    • AMA:
      Dong-Lun Wu. Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials. Mathematical Problems in Engineering. 2019;2019. doi:10.1155/2019/9291534
    • APA:
      Dong-Lun Wu. (2019). Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials. Mathematical Problems in Engineering, 2019. https://doi.org/10.1155/2019/9291534
    • Chicago/Turabian: Author-Date:
      Dong-Lun Wu. 2019. “Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials.” Mathematical Problems in Engineering 2019 (January). doi:10.1155/2019/9291534.
    • Harvard:
      Dong-Lun Wu (2019) ‘Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials’, Mathematical Problems in Engineering, 2019. doi: 10.1155/2019/9291534.
    • Harvard: Australian:
      Dong-Lun Wu 2019, ‘Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials’, Mathematical Problems in Engineering, vol. 2019, viewed 28 September 2020, .
    • MLA:
      Dong-Lun Wu. “Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials.” Mathematical Problems in Engineering, vol. 2019, Jan. 2019. EBSCOhost, doi:10.1155/2019/9291534.
    • Chicago/Turabian: Humanities:
      Dong-Lun Wu. “Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials.” Mathematical Problems in Engineering 2019 (January 1, 2019). doi:10.1155/2019/9291534.
    • Vancouver/ICMJE:
      Dong-Lun Wu. Existence and Multiplicity of Solutions for Sublinear Schrödinger Equations with Coercive Potentials. Mathematical Problems in Engineering [Internet]. 2019 Jan 1 [cited 2020 Sep 28];2019. Available from: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsdoj&AN=edsdoj.2be5b25425644e4bb2b139181ca511fc&custid=s8280428