Existence Of Positive Solutions For A Fractional Laplace Equation Involving Critical Sobolev Exponent

In this paper,we will use variational method to investigate the existence of positive solutions for the following fractional Laplace equation,which is involved with critical Sobolev exponent and has the type where 0<s<1,N>2s,Ω(?)RN is a bounded domain with smooth boundary,and f ∈ H-s(RN),f ≥ 0,λ is a constant.2*(s)=2N/N-2s is the fractional Sobolev critical exponent.We prove that the equation exists two positive solutions when f and λsatisfy some assumptions.