A TOPOLOGICAL CLASSIFICATION OF DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECT

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D. D. BAINOV
S. I. KOSTADINOV
NGUYEN VAN MINH
P. P. ZABREIKO

Abstract




The present paper is concerned with the problem of topological clas- sification of differential equations with impulse effect. Under the assumption that the linear part of the right-hand side of the equation considered has an exponential dichotomy and the nonlinear perturbation is small enough it is proved that for the underlying equations there exist $N + 1$ types topologicall'y,,different from one another.




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How to Cite
BAINOV, D. D., KOSTADINOV, S. I., MINH, N. V., & ZABREIKO, P. P. (1994). A TOPOLOGICAL CLASSIFICATION OF DIFFERENTIAL EQUATIONS WITH IMPULSE EFFECT. Tamkang Journal of Mathematics, 25(1), 15–27. https://doi.org/10.5556/j.tkjm.25.1994.4420
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Papers

References

D. D. Bainov, S. I. Kostadinov and P. P. Zabreiko, "Exponential dichotomy of linear impulsive differential equations in a Banach space", International J. of Theoretical Physics, v. 28(1989), no. 7, 797-814.

Nguyen Van Minh, "On a topological classification of nonautonomous differential equations", Colloquia Mathematica Societaties Janos Bolyai, 53 (1988), 421-426.

J. K. Palmer, "A characterization of exponential dichotomy in terms of topological equivalence", J. Math. Anal. Appl., 69 (1979), No. 1, 8-16.

W. A. Coppel," Dichotomies in Stability Theory", Lecture Notes in Mathematics, v. 629, Springer- Verlag, Berlin, 1978, p.97.

Ju. L. Daleckii and M.G. Krein, "Stability of Solutions of Differential Equations in Banach Space", AMS, Books and Journals in Advanced Mathematics, 1974, p.386.

A. M. Samoilenko and N. A. Perestyuk, "Differential Equations with Impulse Effect", Viica Skola, Kiev, 1987, p. 287 (in Russian).

D. D. Bainov, S. I. Kostadinov, Nguyen Hong Thai and P. P. Zabreiko, "Existence of integral manifolds for impulsive differential equations'', International Journal of Theoretical Physics, 28 (1989), No. 7, 815-833.

M. Golubitsky and V. Guillemin, "Stable Mappings and Their Singularities", Spinger-Verlag, New York-Heideberg-Berlin, 1973. ·

B. Aulbach, "Continuous and Discrete Dynamics near Manifolds of Equilibria, Lecture Notes in Mathematics", v. 1058, Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1984.

D. D. Bainov, S. I. Kostadinov, P. P. Zabreiko and Nguyen Van Minh, "Topological equivalence and exponential dichotomy of linear impulsive equations", to appear.

B. F. Bylov, R. E. Vinograd, D. M. Grobman and V. V. Nemytsky, Theory of Lyapunov Exponents, Nauka, Moscow, 1966 (in Russian).

E. A. Tichonova, "Analogy and homeomorphism of perturbed and unperturbed systems with block- triangular matrix",Differential Eqiations 7 (1970), 1221-1229 (in Russian).