On global transformations of functional-differential equations of the first order

Václav Tryhuk

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 2, page 279-293
  • ISSN: 0011-4642

Abstract

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The paper describes the general form of functional-differential equations of the first order with m ( m ≥ 1 ) delays which allows nontrivial global transformations consisting of a change of the independent variable and of a nonvanishing factor. A functional equation f ( t , u v , u 1 v 1 , ... , u m v m ) = f ( x , v , v 1 , ... , v m ) g ( t , x , u , u 1 , ... , u m ) u + h ( t , x , u , u 1 , ... , u m ) v for u ≠ 0 is solved on ℝ and a method of proof by J. Aczél is applied.

How to cite

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Tryhuk, Václav. "On global transformations of functional-differential equations of the first order." Czechoslovak Mathematical Journal 50.2 (2000): 279-293. <http://eudml.org/doc/30561>.

@article{Tryhuk2000,
abstract = {The paper describes the general form of functional-differential equations of the first order with $m (m\ge 1)$ delays which allows nontrivial global transformations consisting of a change of the independent variable and of a nonvanishing factor. A functional equation \[ f(t, uv, u\_\{1\}v\_\{1\}, \ldots , u\_\{m\}v\_\{m\}) = f(x, v, v\_\{1\}, \ldots , v\_\{m\})g(t, x, u, u\_\{1\}, \ldots , u\_\{m\})u + h(t, x, u, u\_\{1\}, \ldots , u\_\{m\})v \] for $u\ne 0$ is solved on $\mathbb \{R\}$ and a method of proof by J. Aczél is applied.},
author = {Tryhuk, Václav},
journal = {Czechoslovak Mathematical Journal},
keywords = {functional differential equations; ordinary differential equations; global transformations; functional equations in a single variable; functional equations in several variables; functional-differential equations; ordinary differential equations; global transformations; functional equations in a single variable; functional equations in several variables},
language = {eng},
number = {2},
pages = {279-293},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On global transformations of functional-differential equations of the first order},
url = {http://eudml.org/doc/30561},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Tryhuk, Václav
TI - On global transformations of functional-differential equations of the first order
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 2
SP - 279
EP - 293
AB - The paper describes the general form of functional-differential equations of the first order with $m (m\ge 1)$ delays which allows nontrivial global transformations consisting of a change of the independent variable and of a nonvanishing factor. A functional equation \[ f(t, uv, u_{1}v_{1}, \ldots , u_{m}v_{m}) = f(x, v, v_{1}, \ldots , v_{m})g(t, x, u, u_{1}, \ldots , u_{m})u + h(t, x, u, u_{1}, \ldots , u_{m})v \] for $u\ne 0$ is solved on $\mathbb {R}$ and a method of proof by J. Aczél is applied.
LA - eng
KW - functional differential equations; ordinary differential equations; global transformations; functional equations in a single variable; functional equations in several variables; functional-differential equations; ordinary differential equations; global transformations; functional equations in a single variable; functional equations in several variables
UR - http://eudml.org/doc/30561
ER -

References

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  10. The most general transformations of homogeneous linear differential retarded equations of the first order, Arch. Math. (Brno) 16 (1980), 225–230. (1980) MR0594470
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