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Multiple Solutions for a Class of New p ( x )-Kirchhoff Problem without the Ambrosetti-Rabinowitz Conditions

Author

Listed:
  • Bei-Lei Zhang

    (College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China)

  • Bin Ge

    (College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China)

  • Xiao-Feng Cao

    (College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China)

Abstract

In this paper, we consider a nonlocal p ( x ) -Kirchhoff problem with a p + -superlinear subcritical Caratheodory reaction term, which does not satisfy the Ambrosetti–Rabinowitz condition. Under some certain assumptions, we prove the existence of nontrivial solutions and many solutions. Our results are an improvement and generalization of the corresponding results obtained by Hamdani et al. (2020).

Suggested Citation

  • Bei-Lei Zhang & Bin Ge & Xiao-Feng Cao, 2020. "Multiple Solutions for a Class of New p ( x )-Kirchhoff Problem without the Ambrosetti-Rabinowitz Conditions," Mathematics, MDPI, vol. 8(11), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2068-:d:447937
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    References listed on IDEAS

    as
    1. Shapour Heidarkhani & Anderson L. A. De Araujo & Ghasem A. Afrouzi & Shahin Moradi, 2018. "Multiple solutions for Kirchhoff†type problems with variable exponent and nonhomogeneous Neumann conditions," Mathematische Nachrichten, Wiley Blackwell, vol. 291(2-3), pages 326-342, February.
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