Fractional semilinear Neumann problem with critical nonlinearity

In this paper, we consider the following critical fractional semilinear Neumann problem{ (-triangle)(1/2)u + lambda u = u n+1 n-1 , u > 0 in ohm, partial derivative(nu)u = 0 on partial derivative ohm,where ohm subset of R- n (n >= 5) is a smooth bounded domain, lambda > 0 and nu is the outward unit normal to partial derivative ohm. We prove that there exists a constant lambda(0) > 0 such that the above problem admits a minimal energy solution for lambda < lambda(0) . Moreover, if ohm is convex, we show that this solution is constant for sufficiently small lambda.