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

Li Zhou, Chuanxi Zhu and Sergey Shmarev

Advances in Mathematical Physics, 2022, vol. 2022, 1-7

Abstract: In this paper, we consider the following fourth order elliptic Kirchhoff-type equation involving the critical growth of the form Δ2u−a+b∫℠N∇u2dxΔu+Vxu=Iα∗Fufu+λu2∗∗−2u,in ℠N,u∈H2℠N, where a>0, b≥0, λ is a positive parameter, α∈N−2,N, 5≤N≤8, V:℠N⟶℠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=ΔΔu is the biharmonic operator. Under certain assumptions on Vx and fu, we prove that the equation has ground state solutions by variational methods.

Date: 2022
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/amp/2022/5820136.pdf (application/pdf)
http://downloads.hindawi.com/journals/amp/2022/5820136.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:5820136

DOI: 10.1155/2022/5820136

Access Statistics for this article

More articles in Advances in Mathematical Physics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().