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