Geodesic
On global transformations of functional-differential equations of the first order
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 2, pp. 279-293.

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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.
Classification : 34-02, 34C20, 34K05, 34K15, 39B40
Keywords: functional differential equations; ordinary differential equations; global transformations; functional equations in a single variable; functional equations in several variables 
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     author = {Tryhuk, V\'aclav},
     title = {On global transformations of functional-differential equations of the first order},
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     pages = {279--293},
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Tryhuk, Václav. On global transformations of functional-differential equations of the first order. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 2, pp. 279-293. http://geodesic.mathdoc.fr/item/CMJ_2000__50_2_a4/