Normalised solutions for p-Laplacian equations with Lp-supercritical growth

For N >= 3 and 2 < p < N, we find normalised solutions to the equation -Delta pu + (1 +V(x))|u|(p-2)u +lambda u =|u|(q-2)u in R-N |u| 2 = rho in the mass supercritical and Sobolev sub critical case, that is q E (pN+2/N , Np/ N-p ), at least if rho > 0 is small enough. The function V is an element of L-N/p(R-N), which plays the role of potential, is assumed to be non-positive and vanishing at infinity. Moreover, we will prove the compactness of the embedding of the space of radial functions W (1,p) (rad)(R-N ) subset of L-q(R-N) for p is an element of (1, N) and q E (pN+2/N , Np/N-p).