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Systems of conditional differential inequalities of Kato type. (English. Russian original) Zbl 0856.34019
Sib. Math. J. 35, No. 6, 1109-1118 (1994); translation from Sib. Mat. Zh. 35, No. 6, 1253-1263 (1994).
This paper is concerned with the extension of some results of J. Kato on differential inequalities from the scalar case to the $$k$$-dimensional case.

##### MSC:
 34A40 Differential inequalities involving functions of a single real variable
##### Keywords:
differential inequalities
Full Text:
##### References:
 [1] V. Laksmikantham and S. Leela, Differential and Integral Inequalities. Vol. 2, Acad. Press, New York (1969). [2] B. S. Razumikhin, ”On stability of systems with delay,” Prikl. Mat. Mekh.,20, No. 3, 513–518 (1956). [3] B. S. Razumikhin, Stability of Hereditary Systems [in Russian], Nauka, Moscow (1988). [4] J. Kato, ”On Liapunov-Razumikhin type theorems for functional differential equations,” Funct. Ekvac.,16, No. 2, 225–239 (1973). · Zbl 0321.34056 [5] V. M. Matrosov, ”Comparison principle with the Lyapunov vector-function,” Differentsial’nye Uravneniya, I:4, No. 8, 1374–1386; No. 10, 1739–1752 (1968); II:5, No. 7, 1171–1185; No. 12, 2129–2143 (1969). · Zbl 0182.42303 [6] V. M. Matrosov, S. N. Vasil’ev, R. I. Kozlov et al., Inference Algorithms for the Theorems of the Lyapunov-Vector-Function Method [in Russian], Nauka, Novosibirsk (1981). [7] N. A. Karatueva, ”The Lyapunov-vector-function method for systems with aftereffect,” in: Differential Equations and Numerical Methods [in Russian], Nauka, Novosibirsk, 1986, pp. 62–72. · Zbl 0612.34072 [8] V. M. Matrosov, ”On differential equations and inequalities with discontinuous right-hand sides,” Differentsial’nye Uravneniya, I:3, No. 3, 395–409; II:3, No. 5, 839–848 (1967). · Zbl 0166.34104 [9] R. I. Kozlov, ”To the theory of differential equations and inequalities with discontinuous righthand sides,” Differentsial’nye Uravneniya,10, No. 12, 1264–1275 (1974). [10] R. I. Kozlov, ”Vector Lyapunov functions with nontemporal comparison systems and their use in analysis of systems with perturbations,” in: Dynamics of Nonlinear Systems [in Russian], Nauka, Novosibirsk, 1983, pp. 57–78. [11] V. D. Ponomarëv, ”Absolute upper semicontinuity,” Mat. Zametki,22, No. 3, 395–399 (1977). [12] R. I. Kozlov, ”Conditional differential inequalities and their application to qualitative analysis of systems with aftereffect by the Lyapunov-Razumikhin-vector-function method,” in: Abstracts: Qualitative Theory of Differential Equations [in Russian], Riga, 1989, p. 123.
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