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

Myroslav L. Gorbachuk·Valentyna I. Gorbachuk
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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 the field of $p$-adic numbers, the necessary and sufficient conditions on initial data for the Cauchy problem to be well-posed in the class of locally analytic vector-valued functions are given. The result is illustrated by $p$-adic partial differential equations.

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Myroslav L. Gorbachuk, Valentyna I. Gorbachuk. 2003-12-01. On the Cauchy Problem for Differential Equations in a Banach Space over the Field of p-Adic Numbers. II. https://arxiv.org/abs/math/0312026

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