On The Existence Of Solutions To A Class Of Quasilinear Elliptic Equations With Vanishing Potentials

In this paper,we mainly study the existence of solutions for a class of elliptic equations in RN with vanishing potentials.(?)where ?pu=div(|?u|p-2?u),1<p<N,p*=Np/N-p,both V(x)and K(x):RN?R are positive continuous functions which vanish at infinity.By working in new Sobolev spaces,and using variational method,we prove that the equation has at least one nontrivial solution for 2p<q<2p*.As q>2p*,we make additional assumptions about functions V and K:?V·x?0,?K·x?0 for(?)x?RN.Using Pohozaev identity,we prove the nonexistence of nontrivial solution for the problem.