On the Brezis-Nirenberg problem on S3 and a conjecture of Bandle-Benguria

We consider the following Brezis-Nirenberg problem on S-3 -Delta(S3)u = lambda u + u(5) in D, u > 0 in D and u = 0 on aD, where D is a geodesic ball on S-3 with geodesic radius theta(1), and Delta(S3) is the Laplace-Beltrami operator on S3. We prove that for any lambda < -3/4 and for every theta(1) < pi with pi - theta(1) sufficiently small (depending on a), there exists bubbling solution to the above problem. This solves a conjecture raised by Bandle and Benguria [J. Differential Equations 178 (2002) 264-279] and Brezis and Peletier [C. R. Acad. Sci. Paris, Ser. I 339 (2004) 291-394].