Existence of positive solutions for a critical fractional Kirchhoff equation with potential vanishing at infinity

Guangze Gu, Xianhua Tang and Xianyong Yang

Mathematische Nachrichten, 2021, vol. 294, issue 4, 717-730

Abstract: In this paper, we consider the following fractional Kirchhoff equation with critical nonlinearity a+b∫R3(−Δ)s2u2dx(−Δ)su+V(x)u=Q(x)f(u)+|u|2s∗−2u,x∈R3,where a,b>0, (−Δ)s is the fractional Laplace operator with s∈(34,1), V vanishes at infinity and 2s∗=63−2s. Under appropriate assumptions on f, we prove the existence of positive solution by using the variational method.

Date: 2021
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https://doi.org/10.1002/mana.201900273

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Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:294:y:2021:i:4:p:717-730

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