Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A generalization of Peano's existence theorem and flow invariance


Author: Michael G. Crandall
Journal: Proc. Amer. Math. Soc. 36 (1972), 151-155
MSC: Primary 34A15
DOI: https://doi.org/10.1090/S0002-9939-1972-0306586-2
MathSciNet review: 0306586
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ F \subseteq {R^n}$ be closed and $ A:F \to {R^n}$ be continuous. Assuming that for $ y \in F$ the distance from $ y + hAy$ to F is $ o(h)$ as $ h \downarrow 0$, it is shown that for each $ x \in F$ the Cauchy problem $ u' = Au$, $ u(0) = x$, has a solution $ u:[0,{T_x}] \to F$ on some interval $ [0,{T_x}],{T_x} > 0$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34A15

Retrieve articles in all journals with MSC: 34A15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0306586-2
Article copyright: © Copyright 1972 American Mathematical Society