Existence of Infinitely Many High Energy Solutions for a Fourth-Order Kirchhoff Type Elliptic Equation in R³

Ting Xiao, Canlin Gan, Qiongfen Zhang^*

College of Science, Guilin University of Technology, Guilin, China.

DOI: 10.4236/jamp.2020.88120                

Abstract

In this paper, we consider the following fourth-order equation of Kirchhoff type

where a, b > 0 are constants, 3 < p < 5, 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.

Keywords

Fourth-Order Kirchhoff Type Elliptic Equation, Infinitely Many Solutions, Symmetric Mountain Pass Theorem, Variational Methods

Conflicts of Interest

The authors declare that they have no competing interests.

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