On stability of some linear and nonlinear delay differential equations

Journal of Mathematical Analysis and Applications

Volumn 314, Issue 2, 2006, Pages 391-411

  Berezansky, Leonid ^a   Braverman, Elena ^b  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b UNIVERSITY OF CALGARY   (Canada)

Author keywords

Delay equations; Exponential stability; Stability by the first approximation

Indexed keywords

EID: 29144526134     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2005.03.103     Document Type: Article

References (28)

1. R. Bellman K. Cooke Differential-Difference Equations 1963 Academic Press New York
2. N.N. Krasovskii Stability of Motion. Applications of Lyapunov's Second Method to Differential Systems and Equations with Delay 1963 Stanford Univ. Press Stanford, CA
3. V. Kolmanovskii A. Myshkis Introduction to the Theory and Applications of Functional-Differential Equations Math. Appl. vol. 463 1999 Kluwer Acad. Publ. Dordrecht
4. E. Liz R.L. Pouso Existence theory for first order discontinuous functional differential equations Proc. Amer. Math. Soc. 130 2002 3301-3311
5. L. Berezansky E. Braverman Oscillation of a linear delay impulsive differential equations Comm. Appl. Nonlinear Anal. 3 1996 61-77
6. I. Györi M. Pituk Comparison theorems and asymptotic equilibrium for delay differential and difference equations Dynam. Systems Appl. 5 1996 277-302
7. V.B. Kolmanovskii V.R. Nosov Stability of Functional-Differential Equations Math. Sci. Engrg. vol. 180 1986 Academic Press London
8. J.K. Hale S.M. Verduyn Lunel Introduction to Functional Differential Equations Appl. Math. Sci. vol. 99 1993 Springer-Verlag New York
9. T. Yoneyama On the 3 2 -stability theorem for one-dimensional delay-differential equations J. Math. Anal. Appl. 125 1987 161-173
10. T. Krisztin On stability properties for one-dimensional functional-differential equations Funkcial. Ekvac. 34 1991 241-256
11. J.W.H. So J.S. Yu M.P. Chen Asymptotic stability for scalar delay differential equations Funkcial. Ekvac. 39 1996 1-17
12. I. Györi F. Hartung J. Turi Preservation of stability in delay equations under delay perturbations J. Math. Anal. Appl. 220 1998 290-312
13. I. Györi F. Hartung Stability in delay perturbed differential and difference equations Topics in Functional Differential and Difference Equations Lisbon, 1999 Fields Inst. Commun. vol. 29 2001 Amer. Math. Soc. Providence, RI 181-194
14. C. Corduneanu Functional Equations with Causal Operators Stability Control Theory Methods Appl. vol. 16 2002 Taylor & Francis London
15. L. Berezansky Development of N.V. Azbelev's W-method in problems of the stability of solutions of linear functional-differential equations Differ. Uravn. 22 1986 739-750
16. N.V. Azbelev L. Berezansky P.M. Simonov A.V. Chistyakov The stability of linear systems with aftereffect. I Differential Equations 23 1987 493-500
17. V.G. Kurbatov Functional-Differential Operators and Equations Math. Appl. vol. 473 1999 Kluwer Acad. Publ. Dordrecht
18. S.A. Gusarenko Criteria for the stability of a linear functional-differential equation Boundary Value Problems 1987 Perm. Politekh. Inst. Perm 41-45
19. S.A. Gusarenko Conditions for the solvability of problems on the accumulation of perturbations for functional-differential equations Functional-Differential Equations 1987 Perm. Politekh. Inst. Perm 30-40
20. S.A. Gusarenko A.I. Domoshnitskii Asymptotic and oscillation properties of first-order linear scalar functional-differential equations Differential Equations 25 1989 1480-1491
21. N.V. Azbelev P.M. Simonov Stability of Differential Equations with Aftereffect Stability Control Theory Methods Appl. vol. 20 2003 Taylor & Francis London
22. T.A. Burton Perron-type stability theorems for neutral equations Nonlinear Anal. 55 2003 285-297
23. N.V. Azbelev L. Berezansky L.F. Rahmatullina A linear functional-differential equation of evolution type Differential Equations 13 1977 1331-1339
24. M.C. Mackey L. Glass Oscillation and chaos in physiological control systems Science 197 1977 287-289
25. J. Losson M.C. Mackey A. Longtin Solution multistability in first order nonlinear differential delay equations Chaos 3 1993 167-176
26. M.C. Mackey Mathematical models of hematopoietic cell replication and control H.G. Othmer F.R. Adler M.A. Lewis J.C. Dallon The Art of Mathematical Modelling: Case Studies in Ecology, Physiology and Biofluids 1997 Prentice Hall 149-178
27. M. Fan X. Zou Global asymptotic stability of a class of nonautonomous integro-differential systems and applications Nonlinear Anal. 57 2004 111-135
28. L. Berezansky E. Braverman L. Idels Delay differential logistic equations with harvesting Math. Comput. Modeling 40 2004 1509-1525