Abstract
A sufficient condition of exponential stability of regular linear systems with bifurcation on a Banach space is proved.
Similar content being viewed by others
References
Yu. S. Bogdanov, “Application of generalized exponent numbers to the investigation of the stability of an equilibrium point,”Dokl. Akad. Nauk SSSR,158, No. 1, 9–12 (1964).
Yu. S. Bogdanov, “Generalized exponent numbers of nonautonomous systems,”Differents. Uravn.,1, No. 9, 1140–1148 (1965).
Yu. S. Bogdanov, “On the revealing of asymptotic stability by means of smallvd-numbers,”Differents. Uravn.,2, No. 3, 309–313 (1966).
Yu. S. Bogdanov, “Approximate generalized exponent numbers of differential systems,”Differents. Uravn.,2, No. 7, 927–933 (1966).
Yu. S. Bogdanov and M. P. Bogdanova, “A nonlinear analog of Lyapunov transformation,”Differents. Uravn.,3, No. 5, 742–748 (1967).
B. P. Demidovitch,Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).
Yu. L. Daletskii and M. G. Krein,Stability of Solutions of Differential Equations in a Banach Space [in Russian], Nauka, Moscow (1967).
J. Bihari, “A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations,”Acta Math. Acad. Sci. Hung.,7, No. 1, 81–94 (1956).
Additional information
Hanoi Techers’ Training College, Vietnam. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 10, pp. 1417–1424, October, 1999.
Rights and permissions
About this article
Cite this article
Loan, T.T. Lyapunov transformation and stability of differential equations in banach spaces. Ukr Math J 51, 1599–1608 (1999). https://doi.org/10.1007/BF02981692
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02981692