Nonnegative Solutions to a Semilinear Dirichlet Problem in a Ball Are Positive and Radially Symmetric

Authors

Alfonso Castro, Harvey Mudd CollegeFollow
Ratnasingham Shivaji, Mississippi State University

Document Type

Article - postprint

Department

Mathematics (HMC)

Publication Date

1989

Abstract

We prove that nonnegative solutions to a semilinear Dirichlet problem in a ball are positive, and hence radially symmetric. In particular, this answers a question in [3] where positive solutions were proven to be radially symmetric. In section 4 we provide a sufficient condition on the geometry of the domain which ensures that nonnegative solutions are positive in the interior.

Comments

Author's post-print manuscript available for download.

For the publisher's PDF, please visit http://dx.doi.org/10.1080/03605308908820645.

Note: The text is badly transcribed on the publisher's page. See PDF (manuscript or publisher's) for correct title, authors and abstract.

Rights Information

© 1989 Marcel Dekker

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

DOI

10.1080/03605308908820645

Recommended Citation

Castro, Alfonso and R. Shivaji. “Non-negative solutions to a semilinear Dirichlet problem in a ball are positive and radially symmetric,” Comm. in Partial Differential Equations, Vol. 14, No. 8-9, (1989), pp. 1091-1100.