Multiple solutions for fractional Kirchhoff equation with critical or supercritical nonlinearity

Abstract

In this paper, we study the following fractional Kirchhoff equation a+b∫R3|(−Δ)s2u|2dx(−Δ)su+V(x)u=f(x,u)+λ|u|p−2u,inR3,where a,b>0, (−Δ)s is the fractional Laplace operator with p≥2s∗=63−2s and V, f satisfies suitable conditions. We show that the above equation has a ground state solution and a sign-changing solution via Moser iterative method and truncation technique.