Stability of the second order delay differential equations with a damping term

Differential Equations and Dynamical Systems

Volumn 16, Issue 3, 2008, Pages 185-205

  Berezansky, Leonid ^a   Braverman, Elena ^b   Domoshnitsky, Alexander ^c  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b UNIVERSITY OF CALGARY   (Canada)

^c ARIEL UNIVERSITY   (Israel)

Author keywords

Exponential stability; Nonoscillation; Positive fundamental function; Second order delay equations

Indexed keywords

EID: 80053919535     PISSN: 09713514     EISSN: 09746870     Source Type: Journal    
DOI: 10.1007/s12591-008-0012-4     Document Type: Article

References (19)

1. N. V. Azbelev and P. M. Simonov, "Stability of Differential Equations with Aftereffect", Stability and Control: Theory, Methods and Applications, Vol. 20, Taylor & Francis, London, 2003.
2. D. Bainov and A. Domoshnitsky, Stability of a second-order differential equation with retarded argument, Dynamics and Stability of Systems, 9(1994), 145-151.
3. L. Berezansky and E. Braverman, On exponential stability of linear differential equations with several delays, J. Math. Anal. Appl., 324(2006), 1336-1355.
4. L. Berezansky, E. Braverman and A. Domoshnitsky, Positive solutions and stability of a linear ordinary differential equation of the second order with damping term, arXiv: 0807. 2227v1 [math. DS] (July 14, 2008); to appear in Funct. Differ. Equ., 2009.
5. T. A. Burton, "Stability and Periodic Solutions of Ordinary and Functional Differential Equations", Academic Press, Mathematics in Science and Engineering, Vol. 178, 1985.
6. T. A. Burton, "Stability by Fixed Point Theory for Functional Differential Equations", Dover Publications, Mineola, New York, 2006.
7. T. A. Burton, Fixed points, stability, and exact linearization, Nonlinear Anal., 61(2005), 857-870.
8. T. A. Burton and T. Furumochi, Asymptotic behavior of solutions of functional differential equations by fixed point theorems, Dynam. Systems Appl., 11(2002), 499-519.
9. T. A. Burton and L. Hatvani, Asymptotic stability of second order ordinary, functional, and partial differential equations, J. Math. Anal. Appl., 176(1993), 261-281.
10. B. Cahlon and D. Schmidt, Stability criteria for certain secondorder delay differential equations with mixed coefficients, J. Comput. Appl. Math., 170(1994), 79-102.
11. A. Domoshnitsky, Componentwise applicability of Chaplygin's theorem to a system of linear differential equations with delay, Differential Equations, 26(1991), 1254-1259.
12. L. N. Erbe, Q. Kong and B. G. Zhang, "Oscillation Theory for Functional Differential Equations", Marcel Dekker, New York, Basel, 1995.
13. I. Györi and G. Ladas, "Oscillation Theory of Delay Differential Equations", Clarendon Press, Oxford, 1991.
14. V. B. Kolmanovsky and V. R. Nosov, "Stability of Functional Differential Equations," Academic Press, 1986.
15. G. S. Ladde, V. Lakshmikantham and B. G. Zhang, "Oscillation Theory of Differential Equations with Deviating Argument", Marcel Dekker, New York, Basel, 1987.
16. N. Minorski, "Nonlinear Oscillations", van Nostrand, New York, 1962.
17. A. D. Myshkis, "Linear Differential Equations with Retarded Argument", Nauka, Moscow, 1972 (in Russian).
18. S. B. Norkin, "Differential Equations of the Second Order with Retarded Argument", Translation of Mathematical Monographs, AMS, V. 31, Providence, R. I., 1972.
19. B. Zhang, On the retarded Liénard equation, Proc. Amer. Math. Soc., 115(1992), 779-785.