Convergence tests for one scalar differential equation with vanishing delay

Jaromír Baštinec; Josef Diblík; Zdeněk Šmarda

Archivum Mathematicum (2000)

  • Volume: 036, Issue: 5, page 405-414
  • ISSN: 0044-8753

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Baštinec, Jaromír, Diblík, Josef, and Šmarda, Zdeněk. "Convergence tests for one scalar differential equation with vanishing delay." Archivum Mathematicum 036.5 (2000): 405-414. <http://eudml.org/doc/248545>.

@article{Baštinec2000,
author = {Baštinec, Jaromír, Diblík, Josef, Šmarda, Zdeněk},
journal = {Archivum Mathematicum},
keywords = {delay differential equation; asymptotic convergence; point test; integral test},
language = {eng},
number = {5},
pages = {405-414},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Convergence tests for one scalar differential equation with vanishing delay},
url = {http://eudml.org/doc/248545},
volume = {036},
year = {2000},
}

TY - JOUR
AU - Baštinec, Jaromír
AU - Diblík, Josef
AU - Šmarda, Zdeněk
TI - Convergence tests for one scalar differential equation with vanishing delay
JO - Archivum Mathematicum
PY - 2000
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 036
IS - 5
SP - 405
EP - 414
LA - eng
KW - delay differential equation; asymptotic convergence; point test; integral test
UR - http://eudml.org/doc/248545
ER -

References

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  1. 1. O. Arino I. Györi, M. Pituk, Asymptotically diagonal delay differential systems, J. Math. Anal. Appl. 204(1996), 701–728. (1996) MR1422768
  2. 2. O. Arino, and M. Pituk, Convergence in asymptotically autonomouos functional differential equations, J. Math. Anal. Appl. 237(1999), 376–392. (1999) MR1708180
  3. 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) MR0690880
  4. 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) MR0147745
  5. 5. J. Čermák, On the asymptotic behaviour of solutions of certain functional differential equations, Math. Slovaca 48(1998), 187–212. (1998) MR1647674
  6. 6. J. Čermák, The asymptotic bounds of solutions of linear delay systems, J. Math. Anal. Appl. 225(1998), 373–388. (1998) MR1644331
  7. 7. J. Čermák, Asymptotic estimation for functional differential equations with several delays, Arch. Math. 35(1999), 337–345. (1999) MR1744521
  8. 8. J. Čermák, Note on canonical forms for functional differential equations, Math. Pann. 11(2000), 29–39. MR1740739
  9. 9. J. Diblík, A criterion for convergence of solutions of homogeneous delay linear differential equations, Ann. Polon. Math. LXXII. 2(1999), 115–130. (1999) MR1737068
  10. 10. J. Diblík, Asymptotic representation of solutions of equation y ˙ ( t ) = β ( t ) [ y ( t ) y ( t τ ( t ) ) ] , J. Math. Anal. Appl. 217(1998), 200–215. (1998) 
  11. 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) MR1396192
  12. 12. I. Györi, M. Pituk, L^2 -perturbation of a linear delay differential equation, J. Math. Anal. Appl. 195(1995), 415–427. (1995) MR1354552
  13. 13. J. Hale, and S.V. Lunel, Introduction to Functional Differential Equations, Springer-Verlag, 1993. (1993) MR1243878
  14. 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. 15. T. Krisztin, On the rate of convergence of solutions of functional differential equations, Funkcial. Ekvac. 29(1986), 1–10. (1986) Zbl0601.34046MR0865210
  16. 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) Zbl0693.45012MR1031171
  17. 17. K. Murakami, Asymptotic constancy for systems of delay differential equations, Nonl. Analysis, Theory, Methods and Appl. 30(1997), 4595–4606. (1997) Zbl0959.34058MR1603444
  18. 18. S.N. Zhang, Asymptotic behaviour and structure of solutions for equation x ˙ ( t ) = p ( t ) [ x ( t ) x ( t 1 ) ] , J. Anhui University (Natural Science Edition) 2 (1981), 11–21. [In Chinese] (1981) 

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