The Brezis-Nirenberg problem on S

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:178

Article

Bandle, C ; Benguria, R

关键词: nonlinear elliptic boundary value problems critical Sobolev exponent;   

DOI  :  10.1006/jdeq.2001.4006

来源: Elsevier

【 摘 要 】

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.

【 授权许可】

Free