On the Cauchy Problem for Differential Equations in a~Banach Space over the Field of $p$-Adic Numbers
Informatics and Automation, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 99-106
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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.
@article{TRSPY_2004_245_a10,
author = {M. L. Gorbachuk and V. I. Gorbachuk},
title = {On the {Cauchy} {Problem} for {Differential} {Equations} in {a~Banach} {Space} over the {Field} of $p${-Adic} {Numbers}},
journal = {Informatics and Automation},
pages = {99--106},
publisher = {mathdoc},
volume = {245},
year = {2004},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a10/}
}
TY - JOUR AU - M. L. Gorbachuk AU - V. I. Gorbachuk TI - On the Cauchy Problem for Differential Equations in a~Banach Space over the Field of $p$-Adic Numbers JO - Informatics and Automation PY - 2004 SP - 99 EP - 106 VL - 245 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a10/ LA - ru ID - TRSPY_2004_245_a10 ER -
%0 Journal Article %A M. L. Gorbachuk %A V. I. Gorbachuk %T On the Cauchy Problem for Differential Equations in a~Banach Space over the Field of $p$-Adic Numbers %J Informatics and Automation %D 2004 %P 99-106 %V 245 %I mathdoc %U http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a10/ %G ru %F TRSPY_2004_245_a10
M. L. Gorbachuk; V. I. Gorbachuk. On the Cauchy Problem for Differential Equations in a~Banach Space over the Field of $p$-Adic Numbers. Informatics and Automation, Selected topics of $p$-adic mathematical physics and analysis, Tome 245 (2004), pp. 99-106. http://geodesic.mathdoc.fr/item/TRSPY_2004_245_a10/