Remark to transformations of functional-differential equations of the first order

journal article - other

English

Effective sufficient and necessary conditions are given that the functional-differential equation $y'(x)=\sum_{i=0}^n a_i(x)b_i(y(x))\Pi_{j=1}^m \delta_{ij}y(\xi_j(x))+q(x)y(x), x\in I\subseteq R,$ with $m (m\geq 1)$ delays be globally transformable into an equation of the form $u'(t)=\sum_{i=0}^n a_ib_i(u(s))\Pi_{j=1}^m \delta_{ij}u(s+c_j)+qu(s), s\in R,$ with constant coefficients and deviations. Here $b_i, \delta_{ij}$ are nontrivial solutions, in the class of functions continuous at a point, of Cauchy's functional equation $b(uv)=b(u)b(v) (u,v\in R-\{\0}).$

functional differential equations, pointwise transformation, functional equation

TRYHUK, V.

1. 1. 1999

SAV

Bratislava

0139-9918

Mathematica Slovaca

49

4

Slovak Republic

481

494

13