Mountain Pass Solution To A Class Of Quasilinear Equations With Hardy-Sobolev Term On Compact Riemannian Manifolds

In this paper we consider the following quasilinear equation（?） where M is a compact Riemannian manifold with dimension N≥3 without boundary,and x₀∈M.Here a（x）,K（x）and h（x）are continuous functions on M satisfying some further conditions.The operator Δ_p,g is the p-Laplace-Beltrami operator on M associated with the metric g,and dg is the Riemannian distance on（M,g）.Moreover,we assume p ∈（1,N）,s ∈[0,p),and r ∈（p,p*）with（?）.The notion（?）is the critical Hardy-Sobolev component.With the help of Mountain Pass Theorem we get the existence results under different assumptions.