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Zeitschrift für Analysis und ihre Anwendungen


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Volume 15, Issue 2, 1996, pp. 345–356
DOI: 10.4171/ZAA/704

Published online: 1996-06-30

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

A. Augustynowicz[1] and H. Leszczyński[2]

(1) University of Gdansk, Poland
(2) University of Gdansk, Poland

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.

Keywords: Analyticity, iterative methods, Banach contraction principle, Bielecki’s norm

Augustynowicz A., Leszczyński H.: On $x$-Analytic Solutions to the Cauchy Problem for Partial Differential Equations with Retarded Variables. Z. Anal. Anwend. 15 (1996), 345-356. doi: 10.4171/ZAA/704