Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: V. M. Matrosov V. Lakshmikantham, and S. Sivasundaram
Title: Vector Lyapunov functions and stability analysis of nonlinear systems
Additional book information: Kluwer Academic Publishers, Dordrecht, 1991, 172 pp., US$79.00. ISBN 0-7923-1152-3.

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

  • [1] T. A. Burton, Uniform asymptotic stability in functional differential equations, Proc. Amer. Math. Soc. 68 (1978), 195-199. MR 0481371 (58:1489)
  • [2] J. R. Haddock and J. Terjéki, Lyapunov-Razumikhin functions and an invariance principle for functional differential equations, J. Differential Equations 48 (1983), 93-122. MR 692846 (84f:34104)
  • [3] W. Hahn, Theory and application of Lyapunov's direct method, Prentice-Hall, Englewood Cliffs, NJ, 1963. MR 0147716 (26:5230)
  • [4] J. K. Hale, Dynamical systems and stability, J. Math. Anal. Appl. 26 (1969), 39-59. MR 0244582 (39:5896)
  • [5] -, Theory of functional differential equations, Springer, NY, 1977. MR 0508721 (58:22904)
  • [6] D. Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Math., vol. 840, Springer, NY, 1981. MR 610244 (83j:35084)
  • [7] N. N. Krasovskiĭ, Stability of motion, Stanford, Univ. Press, Stanford, CA, 1963.
  • [8] V. Lakshmikantham and S. Leela, Differential and integral inequalities, vols. I, and II, Academic Press, NY, 1969.
  • [9] J. P. LaSalle, Stability theory for ordinary differential equations, J. Differential Equations 4 (1968), 57-65. MR 0222402 (36:5454)
  • [10] A. M. Liapounoff, Problème générale de la stabilité du mouvement, Ann. of Math. Stud., no. 17, Princeton Univ. Press, Princeton, NJ, 1947. (This is a reprint of the 1907 French Translation.)
  • [11] A. M. Lyapunov, General problem of stability of motion, Grostechnizdat, Moscow and Leningrad, 1935. (Russian)
  • [12] G. Makay, On the asymptotic stability in terms of two measures for functional differential equations, Nonlinear Anal. 16 (1991), 721-727. MR 1097328 (92b:34093)
  • [13] M. Marachkov, On a theorem on stability, Bull. Soc. Phys. Math. 12 (1940), 171-174.
  • [14] T. Yoshizawa, Asymptotic behavior of solutions of a system of differential equations, Contrib. Differential Equations 1 (1963), 371-387. MR 0148991 (26:6487)
  • [15] -, Stability theory by Liapunov's second method, Math. Soc. Japan Tokyo, 1966.

Review Information:

Reviewer: T. A. Burton
Journal: Bull. Amer. Math. Soc. 26 (1992), 344-348
DOI: https://doi.org/10.1090/S0273-0979-1992-00275-6
American Mathematical Society