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

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 λ>0. By the technical decomposition of the associated Nehari manifold into three parts Λ+,Λ− and Λ0, 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 Λ+ and Λ−, respectively.