Normalized solution to p-Kirchhoff-type equation in RN

The paper is concerned with the p-Kirchhoff equation -(a+b integral(RN)|del u|(p)dx)Delta(p)u=f(u)-mu u-V(x)u(p-1) in H-1(R-N), (1) where a,b>0. When V(x)=0, p=2 and N >= 3, we obtain that any energy ground state normalized solutions of (1) has constant sign and is radially symmetric monotone with respect to some point in R-N by using some energy estimates. When V(x)not equivalent to 0,p>root 3+1,2p-2< p <= N<2p, under an explicit smallness assumption on V with lim|x|->infinity V(x)=sup(R)(N) V(x), we prove the existence of energy ground state normalized solutions of (1).