Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1996-06-30
On $x$-Analytic Solutions to the Cauchy Problem for Partial Differential Equations with Retarded VariablesA. Augustynowicz and H. Leszczyński (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