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Global structure of solutions for equations of Brezis-Nirenberg type on the unit ball

Published online by Cambridge University Press:  12 July 2007

Yoshitsugu Kabeya
Affiliation:
Department of Applied Mathematics, Miyazaki University, Kibana, Miyazaki 889-2192, Japan
Eiji Yanagida
Affiliation:
Mathematical Institute, Tohoku University, Sendai 980-8578, Japan
Shoji Yotsutani
Affiliation:
Department of Mathematics and Informatics, Ryukoku University, Seta, Otsu 520-2194, Japan

Abstract

The Brezis-Nirenberg equation and the scalar field equation on the three-dimensional unit ball are studied. Under the Robin condition, we show the existence and uniqueness of radial solutions in a unified way. In particular, it is shown that the global structure of solutions changes qualitatively when a parameter in the boundary condition exceeds a certain critical value.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2001

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