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Multiple solutions for Kirchhoff†type problems with variable exponent and nonhomogeneous Neumann conditions

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  • Shapour Heidarkhani
  • Anderson L. A. De Araujo
  • Ghasem A. Afrouzi
  • Shahin Moradi

Abstract

The existence of at least three weak solutions for a class of differential equations with p(x)†Kirchhoff†type and subject to small perturbations of nonhomogeneous Neumann conditions is established under suitable assumptions. Our technical approach is based on variational methods. In addition, an example to illustrate our results is given.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathna:v:291:y:2018:i:2-3:p:326-342
    DOI: 10.1002/mana.201600425
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    Cited by:

    1. Heidarkhani, Shapour & Bohner, Martin & Caristi, Giuseppe & Ayazi, Farahnaz, 2021. "A critical point approach for a second-order dynamic Sturm–Liouville boundary value problem with p-Laplacian," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    2. 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.

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