Abstract
It is proved that the ordinary dichotomy is preserved under perturbations of the impulse matrices of linear impulsive differential equations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Coppel, W. A. (1978).Dichotomies in Stability Theory (Lecture Notes in Mathematics, No. 629), Springer-Verlag.
Elaydi, S., and Hájek, O. (1985). Exponential dichotomy of nonlinear systems of ordinary differential equations, inTrends in Theory and Practice of Nonlinear Analysis, V. Lakshmikantham, ed., North-Holland, Amsterdam, pp. 145–153.
Elaydi, S., and Hájek, O. (1987). Some remarks on nonlinear dichotomy and trichotomy, inNonlinear Analysis and Applications, V. Lakshmikantham, ed., Marcel Dekker, New York, pp. 175–178.
Elaydi, S., and Hájek, O. (1988).Journal of Mathematical Analysis and Applications,129, 362–374.
Elaydi, S., and Hájek, O. (to appear). Exponential dichotomy and trichotomy of nonlinear differential equations.
Milev, N., and Bainov, D. (to appear). Dichotomies for linear impulsive differential equations with variable structure.
Palmer, K. J. (1977). A diagonal dominance criterion for exponential dichotomy,Bulletin of the Australian Mathematical Society,17, 363–374.
Palmer, K. J. (1979a).Journal of Differential Equations,33, 16–25.
Palmer, K. J. (1979b).Journal of Mathematical Analysis and Applications,69, 8–16.
Palmer, K. J. (1982a).Journal of Differential Equations,43, 184–203.
Palmer, K. J. (1982b).Journal of Differential Equations,46, 324–345.
Palmer, K. J. (1984a).Journal of Differential Equations,53, 67–97.
Palmer, K. J. (1984b).Journal of Differential Equations,55, 225–256.
Palmer, K. J. (1987a). A perturbation theorem for exponential dichotomies,Proceedings of the Royal Society of Edinburgh,106A, 25–37.
Palmer, K. J. (1987b). Exponential dichotomies for almost periodic equations,Proceedings of the American Mathematical Society,101, 293–298.
Palmer, K. J. (1988). Exponential dichotomies, the shadowing lemma and transversal homoclinic points, inDynamics Reported, 1, V. Kirchgraber and H. O. Walther, eds., pp. 265–306.
Sacker, R. J., and Sell, G. R. (1974).Journal of Differential Equations,15, 429–458.
Sacker, R. J., and Sell, G. R. (1976a).Journal of Differential Equations,22, 478–496.
Sacker, R. J., and Sell, G. R. (1976b).Journal of Differential Equations,22, 497–522.
Sacker, R. J., and Sell, G. R. (1978).Journal of Differential Equations,27, 106–137.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Milev, N.V., Bainov, D.D. Ordinary dichotomy and perturbations of the impulse matrices of linear impulsive differential equation. Int J Theor Phys 29, 643–653 (1990). https://doi.org/10.1007/BF00672038
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00672038