EXISTENCE OF THE LEAST ENERGY SIGN-CHANGING SOLUTIONS FOR FRACTIONAL BREZIS-NIRENBERG PROBLEM

This paper deals with the following fractional Brezis-Nirenberg problem {(-Delta)(s)u=|u|(2*s-2u)+lambda u, in Omega, u=0, in R-N\Omega, where 2(s)*=2N/N-2s, s is an element of(0,1), ohm is a bounded smooth open connected set in R-N, 0< lambda < lambda(1) and lambda(1) is the first eigenvalue of fractional Laplacian(-triangle)sunder the condition u= 0 in R-N\ohm. We establish the existence of the least energy sign-changing solutions for N >= 5s to the above problem, which includes the lower dimensional case. Our results extend and improve the recent works on the existence of sign-changing solutions established by Cora et al. in [9] and Guo et al. in [13] respectively