Transformations $z(t)=L(t)y(\varphi(t))$ of ordinary differential equations

Title:

Transformations $z(t)=L(t)y(\varphi(t))$ of ordinary differential equations

Creator:

Tryhuk, Václav

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:15d92aa4-8272-4598-ad5f-a1250edf20fc
uuid:15d92aa4-8272-4598-ad5f-a1250edf20fc

Subject:

ordinary differential equations, linear differential equations, transformations, and functional equations

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The paper describes the general form of an ordinary differential equation of an order $n+1$ $(n\ge 1)$ 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 \[ f\biggl (s, w_{00}v_0, \ldots , \sum _{j=0}^n w_{n j}v_j\biggr )=\sum _{j=0}^n w_{n+1 j}v_j + w_{n+1 n+1}f(x,v, v_1, \ldots , v_n), \] where $w_{n+1 0}=h(s, x, x_1, u, u_1, \ldots , u_n)$, $ w_{n+1 1}=g(s, x, x_1, \ldots , x_n, u, u_1, \ldots , u_n)$ and $w_{i j}=a_{i j}(x_1, \ldots , x_{i-j+1}, u, u_1, \ldots , u_{i-j})$ for the given functions $a_{i j}$ is solved on $\mathbb R$, $ u\ne 0.$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

519-529

Source:

Czechoslovak Mathematical Journal | 2000 Volume:50 | Number:3

Harvested from:

CDK

Metadata only:

false