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.
- Larry R. Anderson, Estimates of planar regions of asymptotic stability, Quart. Appl. Math. 36 (1978/79), no. 4, 434–438. MR 520125, DOI https://doi.org/10.1090/S0033-569X-1979-0520125-8
- Larry R. Anderson and Walter Leighton, Liapunov functions for autonomous systems of second order, J. Math. Anal. Appl. 23 (1968), 645–664. MR 229922, DOI https://doi.org/10.1016/0022-247X%2868%2990145-5
J. P. LaSalle and S. Lefschetz, Stability by Liapunov’s direct method, with applications, Academic Press, New York, 1961
- Walter Leighton, Morse theory and Liapunov functions, Rend. Circ. Mat. Palermo (2) 13 (1964), 229–238. MR 180729, DOI https://doi.org/10.1007/BF02849531
- Walter Leighton, On the construction of Liapunov functions for certain autonomous nonlinear differential equations, Contributions to Differential Equations 2 (1963), 367–383 (1963). MR 153927
- Raimond A. Struble, Nonlinear differential equations, International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1961. MR 0130408
L. Anderson, Estimates of planar regions of asymptotic stability, Quart. Appl. Math. 36, 434–438 (1979)
L. Anderson and W. Leighton, Liapunov functions for autonomous systems of second order, J. Math. Anal. Appl. 23, 645–664 (1968)
J. P. LaSalle and S. Lefschetz, Stability by Liapunov’s direct method, with applications, Academic Press, New York, 1961
W. Leighton, Morse theory and Liapunov functions, Rend. Circulo Matem., Ser. 2, 1–10 (1964)
W. Leighton, On the construction of Liapunov functions for certain autonomous nonlinear differential equations, Contrib. Diff. Eqs. 2, 367–383 (1963)
R. Struble, Nonlinear differential equations, McGraw-Hill Book Co., Inc., New York, 1962
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Article copyright:
© Copyright 1981
American Mathematical Society