Existence Of Multiple Positive Solutions For Fractional Laplace Problems With Critical Growth

We consider the following fractional Laplace problems with critical growth:(?) where(-?)s is the fractional Laplace operator,s E(0,1),?(?)RN(N>2s)is a smooth bounded domain,?>0.1<q<2s*:=2N/N-2s,g?C(?).This paper uses the variational method to prove that when g satisfy certian conditions,the problem(*)has multiple positive solutions.We consider the concave power case or the convex power case and these two cases are treated separately.The relation between the number of the local maximum points of the coefficient function of the critical nonlinearity and the number of the positive solutions of the problem(*)are pointed out.