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

Czechoslovak Mathematical Journal (2000)

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

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topTryhuk, 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 -

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## Citations in EuDML Documents

top- Václav Tryhuk, Oldřich Dlouhý, The moving frames for differential equations. II. Underdetermined and functional equations
- Václav Tryhuk, Remark to transformations of functional-differential equations of the first order
- Václav Tryhuk, On transformations $z\left(t\right)=L\left(t\right)y\left(\phi \right(t\left)\right)$ of functional-differential equations
- V. Tryhuk, Equivalence and symmetries of first order differential equations

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