On transformations $z(t)=L(t)y(\varphi (t))$ of functional-differential equations

journal article - other

English

The paper describes the general form of an ordinary differential equation of the order $n+1 (n\geq 1)$ with $m (m\geq 1)$ delays which allows a nontrivial global transformations consisting of a change of the independent variable and of a nonvanishing factor. A functional equation $f(s,W\vec v,W_{(1)}\vec v_{(1)},\ldots,W_{(m)}\vec v_{(m)})=\sum_{i=0}^n w_{n+1 i}v_i+w_{n+1 n+1}f(x,\vec v,\vec v_{(1)},\ldots,\vec v_{(m)}),$ $s,x\in R; W,W_{(1)},\ldots,W_{(m)}$ are real valued $n+1$ by $n+1$ matrices, $\vec v, \vec v_{(j)}\in R^{n+1}; w_{ij}=a_{ij}(x_1,\ldots,x_{i-j+1},u,u_1,\ldots,u_{i-j})$ for a given functions $a_{ij}$ is solved on $R, u\neq 0.$

ordinary differential equation, functional-differential equation, transformation, functional equation

TRYHUK, V.

1. 1. 1999

SAV

Bratislava

0139-9918

Mathematica Slovaca

49

5

Slovak Republic

515

530

16