Ground State Solution for a Fourth Order Elliptic Equation of Kirchhoff Type with Critical Growth in ℝN

Li Zhou and Chuanxi Zhu

Advances in Mathematical Physics, 2022, vol. 2022, issue 1

Abstract: In this paper, we consider the following fourth order elliptic Kirchhoff‐type equation involving the critical growth of the form Δ2u−a+b∫ℝN∇u2dxΔu+Vxu=Iα∗Fufu+λu2∗∗−2u,in ℝN,u∈H2ℝN, where a > 0, b ≥ 0, λ is a positive parameter, α ∈ (N − 2, N), 5 ≤ N ≤ 8, V : ℝN⟶ℝ is a potential function, and Iα is a Riesz potential of order α. Here, 2∗∗ = 2N/(n − 4) with N ≥ 5 is the Sobolev critical exponent, and Δ2u = Δ(Δu) is the biharmonic operator. Under certain assumptions on V(x) and f(u), we prove that the equation has ground state solutions by variational methods.

Date: 2022
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https://doi.org/10.1155/2022/5820136

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:5820136

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