TITLE:
Existence of Infinitely Many High Energy Solutions for a Fourth-Order Kirchhoff Type Elliptic Equation in R3
AUTHORS:
Ting Xiao, Canlin Gan, Qiongfen Zhang
KEYWORDS:
Fourth-Order Kirchhoff Type Elliptic Equation, Infinitely Many Solutions, Symmetric Mountain Pass Theorem, Variational Methods
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.8 No.8,
August
20,
2020
ABSTRACT: In this paper, we consider the following fourth-order equation of Kirchhoff type
where a, b > 0 are constants, 3 p V ∈ C (R3, R); Δ2: = Δ (Δ) is the biharmonic operator. By using Symmetric Mountain Pass Theorem and variational methods, we prove that the above equation admits infinitely many high energy solutions under some sufficient assumptions on V (x). We make some assumptions on the potential V (x) to solve the difficulty of lack of compactness of the Sobolev embedding. Our results improve some related results in the literature.