Multiple solutions to p-Laplacian equation with singularity and cylindrical symmetry

In this paper, we shall investigate the existence of multiple (positive) weak solutions for the Dirichlet problem of the p-Laplacian with singularity and cylindrical symmetry. The results depends heavily on parameters n, p, q, r, s and lambda > 0. By the technical decomposition of the associated Nehari manifold into three parts Lambda(+), Lambda(1) and Lambda(0), and some compactness condition such as (PS) condition or local (PS) condition ((PS)(c) condition) at certain level of energy, we obtain two nonnegative minimizers of the energy functional on Lambda(+) and Lambda(-), respectively. (C) 2003 Elsevier Ltd. All rights reserved.