The Brezis-Nirenberg problem on S

In this paper we study existence and nonexistence of solutions to the Brezis Nirenberg problem for different values of lambda in geodesic spheres on S-3. The picture differs considerably from the one in the Euclidean space. It is shown that large spheres containing the hemisphere have two different type of radial solutions for negative values of lambda. Numerical results indicate that for lambda very small the solutions have a maximum near the boundary, whereas for larger values of lambda the maximum is at the origin. The techniques used area Pohozaev type identities, concentration-compactness lemma and numerical methods. (C) 2002 Elsevier Science.