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

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

2003-05-05

arxiv.org/abs/math/0305074v3

Mathematics

Number Theory

7 pages, LaTeX-2e

Scientific paper

For the Cauchy problem for an operator differential equation of the form $y'(z) = Ay(z)$, where $A$ is a closed linear operator on a Banach space over the completion of an algebraic closure of the field of $p$-adic numbers, a criterion of correct solvability in the class of locally analytic vector-functions is established. It is shown how the Cauchy-Kovalevskaya theorem for $p$-adic partial differential equations may be obtained as a particular case from this criterion.

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