A Class Of Constrained Minimizing Problem With A Sub-critical Perturbation

In this paper,we focus our attention on a constraint minimizing problem for p-Laplacian energy functional with a sub-critical perturbation in RN.We prove that e(a,b)admits at least one minimizer if 0<a<a*:=(?)and ∈ R or a=a*and b>0,where Q is a ground state of the scalar equation-ΔpQ+p/N|Q|p-2Q-|Q|s-2Q=0 with s=p+p2/N.Otherwise,e(a,b)has no minimizer.Furthermore,we also investigate the limiting behavior of the minimizers for e(a,b)as a ↗ a*when 0<a<a*and b<0,as well as the limiting behavior of them as b↘ 0 when b>0 and a=a*.