On transformations of functional-differential equations

Jan Čermák

Displaying similar documents to “On transformations of functional-differential equations”

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

Václav Tryhuk (2000)

Czechoslovak Mathematical Journal

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The paper describes the general form of functional-differential equations of the first order with $m (m \geq 1)$ 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 $u \neq 0$ is solved on $ℝ$ and a method of proof by J. Aczél is applied.

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.

Transformation theory of linear ordinary differential equations -- from local to global investigations

František Neuman (1997)

Archivum Mathematicum

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A survey of investigations of linear differential equations from the point of view of transformations is described. These investigations started in the middle of the last century and continued till the present time. Essential step was done in the fifties by O. Borvka, who started global investigations of the second order equations.

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 $y \neq 0$ , $v \neq 0 .$