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 ?_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.