Ground state solutions for a class of fractional Kirchhoff equations with critical growth

摘要

In this paper,we study the effect of lower order perturbations in the existence of positive solutions to the fractional Kirchhoff equation with critical growth (a+b∫R3|(-△)s/2u|2dx)(-△)su+V(x)u =μ|u|p-1u+|u|2*s-2u,x ∈ R3,where a,b ＞ 0 are constants,μ ＞ 0 is a parameter,s ∈(3/4,1),1 ＜ p ＜ 2*s-1 =3+2s/3-2s,and V:R3 → R is a continuous potential function.For suitable assumptions on V,we show the existence of a positive ground state solution,by using the methods of the Pohozaev-Nehari manifold,Jeanjean's monotonicity trick and the concentration-compactness principle due to Lions (1984).

关键词