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Multiplicity Results of Solutions to the Double Phase Problems of Schrödinger–Kirchhoff Type with Concave–Convex Nonlinearities

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  • Yun-Ho Kim

    (Department of Mathematics Education, Sangmyung University, Seoul 03016, Republic of Korea
    These authors contributed equally to this work.)

  • Taek-Jun Jeong

    (Department of Mathematics Education, Sangmyung University, Seoul 03016, Republic of Korea
    These authors contributed equally to this work.)

Abstract

The present paper is devoted to establishing several existence results for infinitely many solutions to Schrödinger–Kirchhoff-type double phase problems with concave–convex nonlinearities. The first aim is to demonstrate the existence of a sequence of infinitely many large-energy solutions by applying the fountain theorem as the main tool. The second aim is to obtain that our problem admits a sequence of infinitely many small-energy solutions. To obtain these results, we utilize the dual fountain theorem. In addition, we prove the existence of a sequence of infinitely many weak solutions converging to 0 in L ∞ -space. To derive this result, we exploit the dual fountain theorem and the modified functional method.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:60-:d:1306663
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    References listed on IDEAS

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    1. 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.
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