Weight functions for a class of Liapunov functions in the plane
Authors:
Larry R. Anderson and Sarah E. Ducich
Journal:
Quart. Appl. Math. 38 (1981), 497-504
MSC:
Primary 34D20
DOI:
https://doi.org/10.1090/qam/614556
MathSciNet review:
614556
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Abstract: In this paper we give a class of weight functions which generate Liapunov functions for a general second-order differential system. In the special case of a Lienard equation we give conditions under which these weight functions may be chosen so as to improve certain known estimates of regions of asymptotic stability. The procedure is applied to a well-known equation and new estimates are obtained.
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- [3] J. P. LaSalle and S. Lefschetz, Stability by Liapunov's direct method, with applications, Academic Press, New York, 1961
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- [6] R. Struble, Nonlinear differential equations, McGraw-Hill Book Co., Inc., New York, 1962 MR 0130408
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Additional Information
DOI:
https://doi.org/10.1090/qam/614556
Article copyright:
© Copyright 1981
American Mathematical Society
