On a Hartman linearization theorem for a class of ODE with impulse effect

Nonlinear Analysis, Theory, Methods and Applications

Volumn 38, Issue 3, 1999, Pages 307-325

  Fenner, Julio López ^a   Pinto, Manuel ^b  

^a UNIVERSIDAD DE LA FRONTERA   (Chile)

^b UNIVERSITY OF CHILE   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENCE EQUATIONS; NONLINEAR EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; THEOREM PROVING;

HARTMAN LINEARIZATION THEOREM; IMPULSE EFFECT;

LINEARIZATION;

EID: 0033212615     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(98)00198-9     Document Type: Article

References (12)

1. D.D. Bainov, P.S. Simeonov, Impulsive Differential Equations: Asymptotic Properties of the Solutions, World Scientific, Singapore, 1995.
2. W.A. Coppel, Stability and Asymptotic Behaviour of Differential Equations, D.C. Heath, Boston, 1965.
3. J.L. Fenner, M. Pinto, On (h, k) manifolds with asymptotic phase, J. Math. Anal. Appl. 216 (1997) 549-568.
4. J.L. Fenner, On (h, k)-trichotomies and asymptotics of non-autonomous difference systems, Comp. Math. Appl. 33 (10) (1997) 105-124.
5. D.M. Grobman, The topological classification of the vicinity of a singular point in n-dimensional space, Math. USSR-Sb. 56 (1962) 363-367.
6. P. Hartman, Ordinary Differential Equations, Wiley, New York, 1964.
7. V. Lakshmikhantham, D. Bainov, P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
8. R. Naulin, M. Pinto, Roughness of (h, k)-dichotomies, J. Differential Equations 118 (1) (1995) 20-35.
9. K.J. Palmer, A generalization of Hartman's linearization theorem, J. Math. Anal. Appl. 41 (1973) 753-758.
10. M. Pinto, Dichotomies and Asymptotic Formulas for the Solutions of differential equations, J. Math. Anal. Appl. 195 (1995) 16-31.
11. M. Pinto, Dichotomies for differential systems with impulsive effect, Proc. 1st World Congr. of Nonlinear Analysts, Walter De Gruyter, Berlin, 1996, pp. 1181-1192.
12. A.M. Samoilenko, N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.