Xu, H.Y. (2020) Existence of Positive Solutions for the Nonlinear Kirchhoff Type Equations in Rⁿ. Journal of Mathematical Analysis and Applications, 482, Article ID: 123593.
https://doi.org/10.1016/j.jmaa.2019.123593

has been cited by the following article:

• 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.