Skip Navigation

Journal of the London Mathematical Society 1980 s2-22(1):110-116; doi:10.1112/jlms/s2-22.1.110
© 1980 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Ramankutty, P.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© Oxford University Press

Kamke's Uniqueness Theorem

P. Ramankutty

Department of Mathematics, University of Auckland Auckland, New Zealand

A generalization of Kamke's uniqueness theorem in ordinary differential equations is obtained for the limit Cauchy problem, viz x'(t) = f(t, x(t)), x{t) -> x0 as t t0, where f and x take values in an arbitrary normed linear space X and the initial point (t0, x0) is permitted to be on the boundary of the domain of f. Kamke's hypothesis that ||f(t,x)– f(t,y)|| ≤ ø(|t–to|, ||x–,y||) is replaced by a weaker dissipative-type hypothesis formulated in terms of the duality map of X and a semi-inner product derived from it. Even in the scalar case in which X = R, the generalization obtained is still an extension of Kamke's theorem and some of its later analogues.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.