Asymptotic properties of differential equations with advanced argument

Čermák, Jan. "Asymptotic properties of differential equations with advanced argument." Czechoslovak Mathematical Journal 50.4 (2000): 825-837. <http://eudml.org/doc/30602>.

@article{Čermák2000,
abstract = {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.},
author = {Čermák, Jan},
journal = {Czechoslovak Mathematical Journal},
keywords = {functional differential equation; functional (nondifferential) equation; advanced argument; asymptotic behaviour; functional-differential equation; functional (nondifferential) equation; advanced argument; asymptotic behaviour},
language = {eng},
number = {4},
pages = {825-837},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Asymptotic properties of differential equations with advanced argument},
url = {http://eudml.org/doc/30602},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Čermák, Jan
TI - Asymptotic properties of differential equations with advanced argument
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 4
SP - 825
EP - 837
AB - 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.
LA - eng
KW - functional differential equation; functional (nondifferential) equation; advanced argument; asymptotic behaviour; functional-differential equation; functional (nondifferential) equation; advanced argument; asymptotic behaviour
UR - http://eudml.org/doc/30602
ER -

References

top

10.1006/jmaa.1998.6018, J. Math. Anal. Appl. 225 (1998), 373–388. (1998) MR1644331 DOI10.1006/jmaa.1998.6018
10.1006/jmaa.1997.5709, J. Math. Anal. Appl. 217 (1998), 200–215. (1998) MR1492085 DOI10.1006/jmaa.1997.5709
Functional Differential Equations, Springer-Verlag, New York, 1993. (1993)
10.1016/0022-247X(73)90013-9, J. Math. Anal. Appl. 44 (1973), 745–757. (1973) Zbl0289.34115 MR0333405 DOI10.1016/0022-247X(73)90013-9
10.1016/0022-0396(75)90076-5, J. Differential Equations 18 (1975), 1–10. (1975) Zbl0318.34069 MR0387766 DOI10.1016/0022-0396(75)90076-5
The functional differential equation $y^{'} (x) = a y (λ x) + b y (x)$ , Bull. Amer. Math. Soc. 77 (1971), 891–937. (1971) MR0283338
Iterative Functional Equations, Encyclopedia of Mathematics and its Applications, Cambridge University Press, 1990. (1990) MR1067720
Oscillation Theory of Differential Equations with Deviating Argument, Marcel Dekker, Inc., New York, 1987. (1987) MR1017244
On transformations of differential equations and systems with deviating argument, Czechoslovak Math. J. 31(106) (1981), 87–90. (1981) Zbl0463.34051 MR0604115
Transformations and canonical forms of functional-differential equations, Proc. Roy. Soc. Edinburgh 115A (1990), 349–357. (1990) MR1069527
On the terminal value problem for differential equations with deviating arguments, Arch. Math. (Brno) (1985), 43–49. (1985) MR0818306

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Language to use for this widget.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Number of notes per page

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.