A non-existence result for low energy sign-changing solutions of the Brezis-Nirenberg problem in dimensions 4, 5 and 6

We consider the Brezis-Niremberg problem:(Pε){−△u=|u|p−1u+εu in Ω,u=0 on ∂Ω, where Ω is a smooth bounded domain in Rn, n=4,5,6, p+1=2nn−2 is the critical Sobolev exponent and ε is a positive parameter. The main result of the paper generalizes the result of A. Iacopetti and F. Pacella [10]. Precisely we show that there are no low energy sign-changing solutions uε with max⁡uε/min⁡uε→0 or −∞ as ε goes to zero.