Hostname: page-component-76fb5796d-22dnz Total loading time: 0 Render date: 2024-04-26T13:37:05.420Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniqueness of positive solutions for a class of elliptic boundary value problems

Published online by Cambridge University Press:  14 November 2011

Alfonso Castro  and
Ratnasingham Shivaji
Alfonso Castro
Affiliation:
Department of Mathematics, Southwest Texas State University, San Marcos, Texas 78666, U. S. A.
Ratnasingham Shivaji
Affiliation:
Department of Mathematics, Southwest Texas State University, San Marcos, Texas 78666, U. S. A.
Get access Rights & Permissions [Opens in a new window]

Synopsis

Uniqueness of non-negative solutions conjectured in an earlier paper by Shivaji is proved. Our methods are independent of those of that paper, where the problem was considered only in a ball. Further, our results apply to a wider class of nonlinearities.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 98 , Issue 3-4 , 1984 , pp. 267 - 269
Copyright
Copyright © Royal Society of Edinburgh 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Adams, R. A.. Sobolev Spaces (New York: Academic Press, 1975).Google Scholar
2Agmon, S., Douglis, A. and Nirenberg, L.. Estimates near the boundary of solutions of elliptic partial differential equations satisfying general boundary conditions, I. Comm. Pure Appl. Math. 12 (1959), 623–727.CrossRefGoogle Scholar
3Brown, K. J., Ibrahim, M. M. and Shivaji, R.. S-shaped bifurcation curves. Nonlinear Anal. 5 (1981), 475–486.CrossRefGoogle Scholar
4Shivaji, R.. Uniqueness results for a class of positone problems. Nonlinear Anal. 7 (1983), 223–230.CrossRefGoogle Scholar
5Guillemin, V. and Pollack, A.. Differential Topology (New Jersey: Prentice Hall, 1974).Google Scholar