Existence Solutions To Two Class Of Elliptic Systems With Hardy-Sobolev Critical Exponent

In this paper,we deal with two classes of systems of nonlinear singular elliptic equations,invoiving Hardy-Sobolev critical exponents.By variational methods,We mainly study the existence positive solutions to the two class of elliptic systems.More precisely folllwing: Where Ω(?) RN(N≥3)is a bounded domain with smooth boundary (?)Ω,0∈Ω， l<p<N，0≤α<n-p/p,α≤b＜α+1,0<μ≤μ, is the best Hardy constant,λ1,λ2 >0,1<α, β<p*-1,α+β=p*, is the critical SObolev-Hardy exponent,and where α+β=q,λ1,λ2>0,Ω(?)RN is a bounded domain with smooth boundary (?)Ω, 0∈Ω.Our main purposes include the following three steps.First we estimate the energy of systems of nonlinear singular elliptic equations.Then we compare them with the energy of single equation.Finally,by Mountain Pass lemma,we obtain the existence of positive solutions to the systems of nonlinear singular elliptic equations.