Multiplicity Of Positive Solutions For Quasi-linear Elliptic Equations Involving Concave-convex Nonlinearity And Sobolev-Hardy Term

In this paper we investigate the quasi-linear elliptic equations involving concave-convex nonlinearity and Sobolev-Hardy term,where N ≥ 3,1<p<N,0≤ a N-p/p,1≤q<p<r<p*[a]=Np/N-p(a+1),p*[a]is the critical Sobolev-Hardy exponent and the parameters 0 ≤ λ<λ=(N-p/p-a)p,μ≥ 0.Moreover,f and g are sign-changing weight functions.Analysing to the relationship between the Nehari manifold and fibering maps,via the theory of Lusternik-Schnirelmann category,we get some improvement on existence and mul-tiplicity of positive solution:if the parameter μ among the proper range,then the equation admits at least two positive solutions in Wa 1,p(RN);if the parameter μ among a narrower range,then the equation admits at least three positive solutiorns in Wa 1,p(RN).