# On $x$-Analytic Solutions to the Cauchy Problem for Partial Differential Equations with Retarded Variables

### A. Augustynowicz

University of Gdansk, Poland### H. Leszczyński

University of Gdansk, Poland

## Abstract

We prove some existence results for solutions analytic with respect to the spatial variables to first-order equations with a delay and some deviations not only at the function, but also at its derivative. We construct a natural Banach space and a norm which make an adequate integral operator contractive. Due to a useful relation of partial order in this space the main problem is also placed in the theory of monotone iterative techniques.

## Cite this article

A. Augustynowicz, H. Leszczyński, On $x$-Analytic Solutions to the Cauchy Problem for Partial Differential Equations with Retarded Variables. Z. Anal. Anwend. 15 (1996), no. 2, pp. 345–356

DOI 10.4171/ZAA/704