Existence Of Multiple Solutions For A Class Of Fractional Laplacian Equations With Concave And Convex Nonlinearities

In this paper,we study the following fractional laplacian equation (?) where 0<s<1,max{l,q0}<q<2<p<2s*.N>2s,2s*:=2N/2N-2s,q0:=2N/N+2?,?>0 is a constant.The potential function V?C(RN,R)satisfies(Vi)inf V(x)>0;(V2)(?).The energy functional corresponding to the above equation may take infinity value in Hs(RN)and is not C1,because the embedding Hs(RN)(?)L?(RN)is continous only for ??[2,2s*].By establishing one fractional Sobolev embedding result,we first prove the en-ergy functional corresponding to the above equation is C1 on a subspace of Hs(RN).Then,by variational method,we show that the above equation has infinitely many solutions with positive energy and infinitely many solutions with negative energy.