The Brezis-Nirenberg problem with asymptotic analysis of its low energy sign-changing solutions in theory of Sobolev spaces
One of the problems in theory of Sobolev spaces is the Brezis-Nirenberg problem which is appeared in 1983 by Brezis and Nirenberg. In this paper we study the Brezis-Nirenberg problem which is given by the form 
where ε is a real positive parameter and Ω is a smooth bounded domain in Rn, n ≥ 3. That is, in this paper, for a family of sign changing solutions with two bubbles, we in- troduce and investigate some asymptotic analysis.
Keywords: Sobolev space; smooth bounded domain; asymptotic analysis; sign-changing solution
AMS classification: Primary 46E35, 37C60, 35B40
