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Infinitely Many High Energy Solutions for a Fourth-Order Equations of Kirchhoff Type in ℝN

Author

Listed:
  • Belal Almuaalemi

    (Central South University)

  • Haibo Chen

    (Central South University)

  • Sofiane Khoutir

    (USTHB)

Abstract

In this paper we study the following fourth-order elliptic equations of Kirchhoff type $$\Delta^2u - (a+b\int_{\mathbb{R}^N} | \triangledown u|^2dx)\Delta u + V(x)u=f(x, u), \;\;x\in\mathbb{R}^N,$$Δ2u−(a+b∫RN|▽u|2dx)Δu+V(x)u=f(x,u),x∈RN, where Δ2 := Δ(Δ) is the biharmonic operator, a, b > 0 are constants, V ∈ C(ℝN, ℝ) and f ∈ C(ℝN × ℝ, ℝ). Under some appropriate assumptions on V(x) and f(x, u), new results on the existence of infinitely many high energy solutions for the above equation are obtained via Symmetric Mountain Pass Theorem.

Suggested Citation

  • Belal Almuaalemi & Haibo Chen & Sofiane Khoutir, 2020. "Infinitely Many High Energy Solutions for a Fourth-Order Equations of Kirchhoff Type in ℝN," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 121-133, March.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:1:d:10.1007_s13226-020-0388-6
    DOI: 10.1007/s13226-020-0388-6
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    References listed on IDEAS

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    1. Hua Gu & Tianqing An, 2014. "Existence of Multiple Solutions for Fourth-Order Elliptic Problem," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, August.
    2. Fanglei Wang, 2014. "Existence of Solutions for a Coupled System of Second and Fourth Order Elliptic Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-4, October.
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