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 JAMP  Vol.8 No.8 , August 2020
Existence of Infinitely Many High Energy Solutions for a Fourth-Order Kirchhoff Type Elliptic Equation in R3
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.
Cite this paper: Xiao, T. , Gan, C. and Zhang, Q. (2020) Existence of Infinitely Many High Energy Solutions for a Fourth-Order Kirchhoff Type Elliptic Equation in R3. Journal of Applied Mathematics and Physics, 8, 1550-1559. doi: 10.4236/jamp.2020.88120.
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