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

arXivmath/0312026MaRDI QIDQ6473414

M. L. Gorbachuk, V. I. Gorbachuk

Publication date: 1 December 2003

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.

Mathematics Subject Classification ID

Linear differential equations in abstract spaces (34G10) (p)-adic differential equations (12H25)

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