Ground state solution for a critical fractional Kirchhoff equation with L2-constraint

Abstract

In this paper, we study the existence of ground state solution to the following fractional Kirchhoff equation with Sobolev critical exponent in RN:(1+b∫RN|(−Δ)s2u|2dx)(−Δ)su+λu=μ|u|p−2u+|u|2⁎−2u, under the L2-norm constraint:∫RN|u|2dx=a2, where 0<s<1 and N>2s. b,μ are positive numbers and a>0 is a prescribed constant. The existence results are obtained when 2<p<2+4sN.