On a new extension of Liapunov’s direct method to discrete equations
Authors:
L. A. V. Carvalho and Raimundo R. Ferreira
Journal:
Quart. Appl. Math. 46 (1988), 779-788
MSC:
Primary 39A11
DOI:
https://doi.org/10.1090/qam/973390
MathSciNet review:
973390
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Abstract: In this paper, a new procedure is given for applying Liapunov’s direct method to autonomous discrete equations. This procedure is based on an idea that is closely related to Razumikhin’s principle and it includes Liapunov’s direct method as a special case. Examples are given.
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J. P. LaSalle, Stability Theory for Difference Equations—Studies in Ordinary Differential Equations, Stu. in Math. (14), Math. Assoc. of America, Washington, D.C., 1–31, 1977
A. M. Liapunov, Problème Général de la Stabilité du Mouvement, Ann. of Math. Studies, No. 17, Princeton Univ. Press, Princeton, N.J., 1947
B. S. Razumikhin, On the stability of systems with delay, (in Russian) Prikl. Mat. Meh. (20), Inst. Meh. Aka. Nauk CCCP, 500–512, 1956
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Article copyright:
© Copyright 1988
American Mathematical Society
