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

Belal Almuaalemi (), Haibo Chen () and Sofiane Khoutir ()
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Belal Almuaalemi: Central South University
Haibo Chen: Central South University
Sofiane Khoutir: USTHB

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 1, 121-133

Abstract: 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.

Keywords: Fourth-order equations of Kirchhoff type; infinitely many high energy solutions; symmetric mountain pass theorem; 35J20; 35J60 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0388-6

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