On the smoothness of solutions of impulsive autonomous systems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 60, Issue 2, 2005, Pages 311-324

  Akhmet, M U ^a  

^a MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

Author keywords

Analytic dependence of solutions on parameters; Autonomous impulsive differential equation; Differentiable dependence of solutions on parameters

Indexed keywords

DIFFERENTIAL EQUATIONS; FUNCTIONS; METHOD OF MOMENTS; NONLINEAR SYSTEMS; THEOREM PROVING;

ANALYTIC DEPENDENCE OF SOLUTIONS ON PARAMETERS; ANALYTIC FUNCTIONS; AUTONOMOUS IMPULSIVE DIFFERENTIAL EQUATIONS; DIFFERENTIABLE DEPENDENCE OF SOLUTIONS ON PARAMETERS;

AUTONOMOUS AGENTS;

EID: 10044282936     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.08.028     Document Type: Article

References (21)

1. M.U. Akhmet, On the general problem of stability for impulsive differential equations, J. Math. Anal. Appl. 288 (2003)182-198.
2. M.U. Akhmetov, N.A. Perestyuk, Asymptotic representation of solutions of regularly perturbed systems of differential equations with a nonclassical right-hand side, Ukr. Math. J. 43 (1991) 1209-1214.
3. M.U. Akhmetov, N.A. Perestyuk, Differential properties of solutions and integral surfaces for nonlinear pulse systems, Differential Equations 28 (1992) 445-453.
4. A. Andronov, G. Neumark, Sur les mouvements des modsés idéalisés d'horloge ayant deux degrés de liberté. Horloge pré-galiléenne, C. R. (Dokl.) Acad. Sci. URSS (N.S.) 50 (1946) 17-20 (in French).
5. N.N. Bautin, The dynamical theory of clock movements without constructive stopping of the escape wheel instantaneous impulse, Inzh. Sb. 21 (1955) 3-31 (in Russian).
6. E.A. Coddington, N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill Inc., New York, 1955.
7. J.V. Devi, A.S. Vatsala, Generalized quasilinearization for an impulsive differential equation with variable moments of impulse, Dyn, Systems Appl. 12 (2003) 369-382.
8. A.B. Dishliev, D.D. Bainov, Differentiability on a parameter and initial condition of the solution of a system of differential equations with impulses, Osterreich. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II196 69-96.
9. M. Frigon, D. O'Regan, Impulsive differential equations with variable times, Nonlinear Analysis 26 (1996) 1913-1922.
10. J. Guckenheimer, P. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer, New York, 1983.
11. A. Halanay, D. Wexler, Qualitative Theory of Impulsive Systems, Republici Socialiste Romania, Bucuresti, 1968.
12. P. Hartman, Ordinary Differential Equations, Wiley, New York, 1964.
13. C.S. Hsu, Impulsive parametric exitation: theory, Trans. ASME, Ser. E. J. Appl. Mech. 39 (1972) 551-558.
14. N.M. Krylov, N.N. Bogolyubov, Introduction to Nonlinear Mechanics, Acad. Nauk Ukrainy, Kiev, 1937.
15. V Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
16. V. Lakshmikantham, X. Liu, On quasistability for impulsive differential equations, Nonlinear Analysis 13 (1989) 819-828.
17. N. Minorsky, Nonlinear Oscillations, D. Van Nostrand Company Inc., Princeton, London, New York, 1962.
18. R.F. Nagaev, D.G. Rubisov, Impulse motions in a one-dimensional system in a gravitational force field, Sov. Appl. Mech. 26 (1990) 885-890.
19. T. Pavlidis, A new model for simple neural nets and its application in the design of a neural oscillator, Bull. Math. Biophys. 27 (1965) 215-229.
20. A.M. Samoilenko, N.A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore, 1995.
21. P.S. Simeonov, D.D. Bainov, Differentiability of solutions of systems with impulse effect with respect to initial data and parameter, Proc. Edinburgh Math. Soc. 31 (2) (1988) 353-368.