Existence Of Positive Solutions For Elliptic Systems With Critical Sobolev Exponents And Hardy Potentials

In this paper,A Neumann boundary problem is investigated,which involves critical Sobolev exponents and Hardy potentials where parameters λ1,λ2>0,0<μ<μ,α,β>1 satisfying α + β = 2*,μ:=(N-2/2)2 is the best Hardy coistant,2*:=2N/N-2 is the Sobolev critical exponent.Ω is an open bounded domain in RN(N ≥ 3)with smooth boundary(?)Ω,0∈(?)Ω v denotes the unit outward normal of(?)Ω.Using the mountain pass lemma without Palais-Smale condition and maximum principle,under some conditions on λ1,λ2,μ,the existence of a positive solution to the system is established.