|
Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2004, Volume 245, Pages 99–106
(Mi tm176)
|
|
|
|
On the Cauchy Problem for Differential Equations in a Banach Space over the Field of $p$-Adic Numbers
M. L. Gorbachuk, V. I. Gorbachuk Institute of Mathematics, Ukrainian National Academy of Sciences
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 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.
Received in October 2003
Citation:
M. L. Gorbachuk, V. I. Gorbachuk, “On the Cauchy Problem for Differential Equations in a Banach Space over the Field of $p$-Adic Numbers”, Selected topics of $p$-adic mathematical physics and analysis, Collected papers. Dedicated to the 80th birthday of academician Vasilii Sergeevich Vladimirov, Trudy Mat. Inst. Steklova, 245, Nauka, MAIK «Nauka/Inteperiodika», M., 2004, 99–106; Proc. Steklov Inst. Math., 245 (2004), 91–97
Linking options:
https://www.mathnet.ru/eng/tm176 https://www.mathnet.ru/eng/tm/v245/p99
|
Statistics & downloads: |
Abstract page: | 326 | Full-text PDF : | 138 | References: | 66 |
|