Liapunov fundtions and global existence without uniqueness
Author:
Stephen R. Bernfeld
Journal:
Proc. Amer. Math. Soc. 25 (1970), 571-577
MSC:
Primary 34.04
DOI:
https://doi.org/10.1090/S0002-9939-1970-0259211-1
MathSciNet review:
0259211
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Abstract | References | Similar Articles | Additional Information
Abstract: In a recent paper J. Kato and A. Strauss characterized the global existence of solutions of an ordinary differential equation in terms of Liapunov functions in which they assumed the right hand side of the differential equation is locally Lipschitz. In the present paper a characterization of global existence of an ordinary differential equation is found in which the right hand side is merely continuous. The construction of the Liapunov functions depend heavily upon the properties of solution funnels due to the nonuniqueness of solutions.
- Junji Kato and Aaron Strauss, On the global existence of solutions and Liapunov functions, Ann. Mat. Pura Appl. (4) 77 (1967), 303–316 (English, with Italian summary). MR 226130, DOI https://doi.org/10.1007/BF02416946
- George R. Sell, On the fundamental theory of ordinary differential equations, J. Differential Equations 1 (1965), 370–392. MR 176130, DOI https://doi.org/10.1016/0022-0396%2865%2990014-8
- Aaron Strauss and James A. Yorke, On the fundamental theory of differential equations, SIAM Rev. 11 (1969), 236–246. MR 247162, DOI https://doi.org/10.1137/1011037
- Taro Yoshizawa, Stability theory by Liapunov’s second method, Publications of the Mathematical Society of Japan, No. 9, The Mathematical Society of Japan, Tokyo, 1966. MR 0208086
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Additional Information
Keywords:
Global existence of solutions,
Liapunov functions,
nonuniqueness of solutions,
solution funnels,
initial-value problem
Article copyright:
© Copyright 1970
American Mathematical Society