Weight functions for a class of Liapunov functions in the plane-Reference-Cited by-同舟云学术

Weight functions for a class of Liapunov functions in the plane

Published:1981 Issue:4 Volume:38 Page:497-504
ISSN:0033-569X
Container-title:Quarterly of Applied Mathematics
language:en
Short-container-title:Quart. Appl. Math.

Author:

Anderson Larry R.,Ducich Sarah E.

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Link

http://www.ams.org/qam/1981-38-04/S0033-569X-1981-0614556-6/S0033-569X-1981-0614556-6.pdf

Reference6 articles.

1. Estimates of planar regions of asymptotic stability;Anderson, Larry R.;Quart. Appl. Math.,1978

2. Liapunov functions for autonomous systems of second order;Anderson, Larry R.;J. Math. Anal. Appl.,1968

3. J. P. LaSalle and S. Lefschetz, Stability by Liapunov’s direct method, with applications, Academic Press, New York, 1961

4. Morse theory and Liapunov functions;Leighton, Walter;Rend. Circ. Mat. Palermo (2),1964

5. On the construction of Liapunov functions for certain autonomous nonlinear differential equations;Leighton, Walter;Contributions to Differential Equations,1963

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