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

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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 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.