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

Václav Tryhuk

Displaying similar documents to “On global transformations of functional-differential equations of the first order”

On global transformations of ordinary differential equations of the second order

Václav Tryhuk (2000)

Czechoslovak Mathematical Journal

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The paper describes the general form of an ordinary differential equation of the second order which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form $f (t, v y, w y + u v z) = f (x, y, z) u^{2} v + g (t, x, u, v, w) v z + h (t, x, u, v, w) y + 2 u w z$ is solved on $ℝ$ for $y \neq 0$ , $v \neq 0 .$

Remark to transformations of linear differential and functional-differential equations

Václav Tryhuk (2000)

Czechoslovak Mathematical Journal

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For linear differential and functional-differential equations of the $n$ -th order criteria of equivalence with respect to the pointwise transformation are derived.

On transformations of functional-differential equations

Jan Čermák (1993)

Archivum Mathematicum

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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 $τ (x) = λ x$ . 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...