# Associated Spaces Defined by Ordinary Differential Equations

### Wolfgang Tutschke

Technische Universität Graz, Austria### Le Thu Hoai

Faculty of Applied Mathematics and Informatics, Hanoi, Vietnam

## Abstract

The paper deals with initial value problems for desired functions $u(t,x)$ depending on the time $t$ and one spacelike variable $x$. In case the initial function $φ(x)$ satisfies an associated (ordinary) differential equation, the solution $u(t,x)$ satisfies the associated differential equation for each $t$. If the general solution of the associated differential equation is known, one gets a system of ordinary differential equations for the desired coefficients depending on $t$. In any case, the solution can be obtained as fixed point of a related integro-differential operator.

## Cite this article

Wolfgang Tutschke, Le Thu Hoai, Associated Spaces Defined by Ordinary Differential Equations. Z. Anal. Anwend. 25 (2006), no. 3, pp. 385–392

DOI 10.4171/ZAA/1295