Convergence tests for one scalar differential equation with vanishing delay
Baštinec, Jaromír ; Diblík, Josef ; Šmarda, Zdeněk
Archivum Mathematicum, Tome 036 (2000), p. 405-414 / Harvested from Czech Digital Mathematics Library
Publié le : 2000-01-01
Classification:  34K05,  34K25
@article{107753,
     author = {Jarom\'\i r Ba\v stinec and Josef Dibl\'\i k and Zden\v ek \v Smarda},
     title = {Convergence tests for one scalar differential equation with vanishing delay},
     journal = {Archivum Mathematicum},
     volume = {036},
     year = {2000},
     pages = {405-414},
     zbl = {1090.34596},
     mrnumber = {1822808},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107753}
}
Baštinec, Jaromír; Diblík, Josef; Šmarda, Zdeněk. Convergence tests for one scalar differential equation with vanishing delay. Archivum Mathematicum, Tome 036 (2000) pp. 405-414. http://gdmltest.u-ga.fr/item/107753/

1. O. Arino I. Györi; M. Pituk Asymptotically diagonal delay differential systems, J. Math. Anal. Appl. 204(1996), 701–728. (1996) | MR 1422768

2. O. Arino; And M. Pituk Convergence in asymptotically autonomouos functional differential equations, J. Math. Anal. Appl. 237(1999), 376–392. (1999) | MR 1708180

3. F.V. Atkinson; And J.R. Haddock Criteria for asymptotic constancy of solutions of functional differential equations, J. Math. Anal. Appl. 91(1983), 410–423. (1983) | MR 0690880

4. R. Bellman; And K.L. Cooke Differential-difference Equations, Mathematics in science and engineering, A series of Monographs and Textbooks, New York, London, Academic Press, 1963. (1963) | MR 0147745

5. J. Čermák On the asymptotic behaviour of solutions of certain functional differential equations, Math. Slovaca 48(1998), 187–212. (1998) | MR 1647674

6. J. Čermák The asymptotic bounds of solutions of linear delay systems, J. Math. Anal. Appl. 225(1998), 373–388. (1998) | MR 1644331

7. J. Čermák Asymptotic estimation for functional differential equations with several delays, Arch. Math. 35(1999), 337–345. (1999) | MR 1744521

8. J. Čermák Note on canonical forms for functional differential equations, Math. Pann. 11(2000), 29–39. | MR 1740739

9. J. Diblík A criterion for convergence of solutions of homogeneous delay linear differential equations, Ann. Polon. Math. LXXII. 2(1999), 115–130. (1999) | MR 1737068

10. J. Diblík Asymptotic representation of solutions of equation $\dot{y}(t) = \beta(t)[y(t) − y(t − \tau (t))]$, J. Math. Anal. Appl. 217(1998), 200–215. (1998)

11. I. Györi; M. Pituk Comparison theorems and asymptotic equilibrium for delay differential and difference equations, Dynamic Systems and Appl. 5(1996), 277–302. (1996) | MR 1396192

12. I. Györi; M. Pituk L^2 -perturbation of a linear delay differential equation, J. Math. Anal. Appl. 195(1995), 415–427. (1995) | MR 1354552

13. J. Hale; And S.V. Lunel Introduction to Functional Differential Equations, Springer-Verlag, 1993. (1993) | MR 1243878

14. T. Krisztin Asymptotic estimation for functional differential equations via Lyapunov functions, Colloquia Mathematica Societatis János Bolyai, 53, Qualitative theory of differential equations, Szeged, 1986, 1–12. (1986)

15. T. Krisztin On the rate of convergence of solutions of functional differential equations, Funkcial. Ekvac. 29(1986), 1–10. (1986) | MR 0865210 | Zbl 0601.34046

16. T. Krisztin A note on the convergence of the solutions of a linear functional differential equation, J. Math. Anal. Appl. 145(1990), 17–25. (1990) | MR 1031171 | Zbl 0693.45012

17. K. Murakami Asymptotic constancy for systems of delay differential equations, Nonl. Analysis, Theory, Methods and Appl. 30(1997), 4595–4606. (1997) | MR 1603444 | Zbl 0959.34058

18. S.N. Zhang Asymptotic behaviour and structure of solutions for equation $\dot{x}(t) = p(t)[x(t) − x(t − 1)]$, J. Anhui University (Natural Science Edition) 2 (1981), 11–21. [In Chinese] (1981)