Ground state solutions for singular p-Laplacian equation in RN

In this work, we study the ground state solution for the class of singular quasilinear elliptic problem of the form -div(vertical bar x vertical bar(-ap)vertical bar del u vertical bar(p-2)del u) + h(vertical bar x vertical bar)vertical bar u vertical bar(m-2)u = H(vertical bar x vertical bar)vertical bar u vertical bar(q-2)u, x is an element of R-N. where 1 < p < N, a < N-p/p and h(r), H(r) >= 0. We prove the compactly embedding results of the weighted Z = D-a,r(1,p) (R-N) boolean AND L-h,r(m) (R-N) space of radially symmetric functions and then obtain the existence of nontrivial ground state solution. Crown Copyright (C) 2008 Published by Elsevier Inc. All rights reserved.