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Multiplicity of Radially Symmetric Small Energy Solutions for Quasilinear Elliptic Equations Involving Nonhomogeneous Operators

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  • Jun Ik Lee

    (Department of Mathematics Education, Sangmyung University, Seoul 03016, Korea)

  • Yun-Ho Kim

    (Department of Mathematics Education, Sangmyung University, Seoul 03016, Korea)

Abstract

We investigate the multiplicity of radially symmetric solutions for the quasilinear elliptic equation of Kirchhoff type. This paper is devoted to the study of the L ∞ -bound of solutions to the problem above by applying De Giorgi’s iteration method and the localization method. Employing this, we provide the existence of multiple small energy radially symmetric solutions whose L ∞ -norms converge to zero. We utilize the modified functional method and the dual fountain theorem as the main tools.

Suggested Citation

  • Jun Ik Lee & Yun-Ho Kim, 2020. "Multiplicity of Radially Symmetric Small Energy Solutions for Quasilinear Elliptic Equations Involving Nonhomogeneous Operators," Mathematics, MDPI, vol. 8(1), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:1:p:128-:d:308920
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    References listed on IDEAS

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    1. Giovany M. Figueiredo & Jefferson A. Santos, 2017. "Existence of least energy nodal solution with two nodal domains for a generalized Kirchhoff problem in an Orlicz–Sobolev space," Mathematische Nachrichten, Wiley Blackwell, vol. 290(4), pages 583-603, March.
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    Cited by:

    1. Yun-Ho Kim & Taek-Jun Jeong, 2023. "Multiplicity Results of Solutions to the Double Phase Problems of Schrödinger–Kirchhoff Type with Concave–Convex Nonlinearities," Mathematics, MDPI, vol. 12(1), pages 1-35, December.

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