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

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Abstract

In this paper we study the following fourth-order elliptic equations of Kirchhoff type

$$\Delta^2u - (a+b\int_{\mathbb{R}^N} | \triangledown u|^2dx)\Delta u + V(x)u=f(x, u), \;\;x\in\mathbb{R}^N,$$

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.

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Acknowledgement

This work was supported by the Natural Science Foundation of China (11671403) and the Mathematics and Interdisciplinary Science project of CSU.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, P. R. China

    Belal Almuaalemi & Haibo Chen

  2. Faculty of Mathematics, USTHB, BP 32 El Alia, Bab Ezzouar, 16111, Algiers, Algeria

    Sofiane Khoutir

Authors
  1. Belal Almuaalemi
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  2. Haibo Chen
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  3. Sofiane Khoutir
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Correspondence to Belal Almuaalemi.

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Almuaalemi, B., Chen, H. & Khoutir, S. Infinitely Many High Energy Solutions for a Fourth-Order Equations of Kirchhoff Type in ℝN. Indian J Pure Appl Math 51, 121–133 (2020). https://doi.org/10.1007/s13226-020-0388-6

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  • DOI: https://doi.org/10.1007/s13226-020-0388-6

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