The Existence Of Positive Solutions Of A Fractional Laplacian Equation With Critical Sobolev Growth

In this paper,we study the exdstence of positive solutions of the following frac-tional Laplacian equation with Sobolev critical exponent where f H-s((RN).s ?(0,1),2*:= 2N/N-2s.Under appropriate assumptions on the function f,we transform the question of finding solutions into proving a infimum problem.Secondly,we prove the infmum is attained by one function.At last,we prove the existence of solutions of our equation by virture of Ekeland's variational principle.Compared with many corresponding Laplacian equations,the proof of nonlocal fractional Laplacian equations are more difficult to deal with.