Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
functional differential equation; functional (nondifferential) equation; advanced argument; asymptotic behaviour
functional differential equation; functional (nondifferential) equation; advanced argument; asymptotic behaviour
Summary:
The paper discusses the asymptotic properties of solutions of the scalar functional differential equation \[ y^{\prime }(x)=ay(\tau (x))+by(x),\qquad x\in [x_0,\infty ) \] of the advanced type. We show that, given a specific asymptotic behaviour, there is a (unique) solution $y(x)$ which behaves in this way.
References:
[1] J. Čermák: The asymptotic bounds of linear delay systems. J. Math. Anal. Appl. 225 (1998), 373–388. DOI 10.1006/jmaa.1998.6018 | MR 1644331
[2] 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. DOI 10.1006/jmaa.1997.5709 | MR 1492085
[3] J. K. Hale and S. M. Verduyn Lunel: Functional Differential Equations. Springer-Verlag, New York, 1993.
[4] M. L. Heard: Asymptotic behavior of solutions of the functional differential equation $x^{\prime }(t)=ax(t)+bx(t^{\alpha })$, $\alpha >1$. J. Math. Anal. Appl. 44 (1973), 745–757. DOI 10.1016/0022-247X(73)90013-9 | MR 0333405 | Zbl 0289.34115
[5] M. L. Heard: A change of variables for functional differential equations. J. Differential Equations 18 (1975), 1–10. DOI 10.1016/0022-0396(75)90076-5 | MR 0387766 | Zbl 0318.34069
[6] T. Kato and J. B. Mcleod: The functional differential equation $y^{\prime }(x)=ay(\lambda x)+by(x)$. Bull. Amer. Math. Soc. 77 (1971), 891–937. MR 0283338
[7] M. Kuczma, B. Choczewski and R. Ger: Iterative Functional Equations. Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1990. MR 1067720
[8] G. S. Ladde, V. Lakshmikantham and B. G. Zhang: Oscillation Theory of Differential Equations with Deviating Argument. Marcel Dekker, Inc., New York, 1987. MR 1017244
[9] F. Neuman: On transformations of differential equations and systems with deviating argument. Czechoslovak Math. J. 31(106) (1981), 87–90. MR 0604115 | Zbl 0463.34051
[10] F. Neuman: Transformations and canonical forms of functional-differential equations. Proc. Roy. Soc. Edinburgh 115A (1990), 349–357. MR 1069527
[11] V. A. Staikos and P. Ch. Tsamatos: On the terminal value problem for differential equations with deviating arguments. Arch. Math. (Brno) (1985), 43–49. MR 0818306
Search
Partner of
