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Tr. Mat. Inst. Steklova, 2004, Volume 245, Pages 99–106 (Mi tm176)  

On the Cauchy Problem for Differential Equations in a Banach Space over the Field of $p$-Adic Numbers

M. L. Gorbachuk, V. I. Gorbachuk

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: For an operator-differential equation of the form $y^{(m)}(z) = Ay(z)$, where $A$ is a closed linear operator on a Banach space over the field of $p$-adic numbers, conditions on the initial data are given that are necessary and sufficient for the Cauchy problem to be well-posed in the class of locally analytic vector-valued functions. The result is illustrated by $p$-adic partial differential equations.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2004, 245, 91–97

Bibliographic databases:

UDC: 517.94+512.625.5
Received in October 2003

Citation: M. L. Gorbachuk, V. I. Gorbachuk, “On the Cauchy Problem for Differential Equations in a Banach Space over the Field of $p$-Adic Numbers”, Selected topics of $p$-adic mathematical physics and analysis, Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov, Tr. Mat. Inst. Steklova, 245, Nauka, MAIK Nauka/Inteperiodika, M., 2004, 99–106; Proc. Steklov Inst. Math., 245 (2004), 91–97

Citation in format AMSBIB
\Bibitem{GorGor04}
\by M.~L.~Gorbachuk, V.~I.~Gorbachuk
\paper On the Cauchy Problem for Differential Equations in a~Banach Space over the Field of $p$-Adic Numbers
\inbook Selected topics of $p$-adic mathematical physics and analysis
\bookinfo Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov
\serial Tr. Mat. Inst. Steklova
\yr 2004
\vol 245
\pages 99--106
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm176}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2099873}
\zmath{https://zbmath.org/?q=an:1105.34320}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2004
\vol 245
\pages 91--97


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