# On transformations of functional-differential equations

Archivum Mathematicum (1993)

- Volume: 029, Issue: 3-4, page 227-234
- ISSN: 0044-8753

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topČermák, Jan. "On transformations of functional-differential equations." Archivum Mathematicum 029.3-4 (1993): 227-234. <http://eudml.org/doc/247427>.

@article{Čermák1993,

abstract = {The paper contains applications of Schrőder’s equation to differential equations with a deviating argument. There are derived conditions under which a considered equation with a deviating argument intersecting the identity $y=x$ can be transformed into an equation with a deviation of the form $\tau (x)=\lambda x$. Moreover, if the investigated equation is linear and homogeneous, we introduce a special form for such an equation. This special form may serve as a canonical form suitable for the investigation of oscillatory and asymptotic properties of the considered equation.},

author = {Čermák, Jan},

journal = {Archivum Mathematicum},

keywords = {Functional-differential equation; singular case; transformation; canonical form; differential equations with deviating arguments; oscillatory and asymptotic properties},

language = {eng},

number = {3-4},

pages = {227-234},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {On transformations of functional-differential equations},

url = {http://eudml.org/doc/247427},

volume = {029},

year = {1993},

}

TY - JOUR

AU - Čermák, Jan

TI - On transformations of functional-differential equations

JO - Archivum Mathematicum

PY - 1993

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 029

IS - 3-4

SP - 227

EP - 234

AB - The paper contains applications of Schrőder’s equation to differential equations with a deviating argument. There are derived conditions under which a considered equation with a deviating argument intersecting the identity $y=x$ can be transformed into an equation with a deviation of the form $\tau (x)=\lambda x$. Moreover, if the investigated equation is linear and homogeneous, we introduce a special form for such an equation. This special form may serve as a canonical form suitable for the investigation of oscillatory and asymptotic properties of the considered equation.

LA - eng

KW - Functional-differential equation; singular case; transformation; canonical form; differential equations with deviating arguments; oscillatory and asymptotic properties

UR - http://eudml.org/doc/247427

ER -

## References

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- Some observations on the asymptotic behaviors of the solutions of the equation ${x}^{\text{'}}\left(t\right)=A\left(t\right)x\left(\lambda t\right)+B\left(t\right)x\left(t\right),\lambda >0$, J.Math.Anal.Appl. 67 (1979), 483–489. (1979) MR0528702
- Regular iteration of real and complex functions, Acta Math. 100 (1958), 203–258. (1958) Zbl0145.07903MR0107016
- The most general transformation of homogeneous retarded linear differential equations of the $n$-th order, Math.Slovaka 33 (1983), 15–21. (1983) Zbl0514.34058MR0689272

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