Linear differential equation with inhomogeneity in the form of a formal power series over a ring with non-Archimedean valuation
UDC 517.922 Consider the linear nonhomogeneous differential equation of $m$-th order with constant coefficients from the valuation ring $K$ of a non-Archimedean field. We get sufficient conditions of uniqueness and existence for the solution from the ring of formal power series $K[[x]]$ of thi...
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| Дата: | 2026 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Українська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2026
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/7287 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | UDC 517.922
Consider the linear nonhomogeneous differential equation of $m$-th order with constant coefficients from the valuation ring $K$ of a non-Archimedean field. We get sufficient conditions of uniqueness and existence for the solution from the ring of formal power series $K[[x]]$ of this equation. Also the fundamental solution of the equation is obtained and it is shown that the convolution of the fundamental solution and a non-homogeneity is a unique solution of the equation. |
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| DOI: | 10.37863/umzh.v74i11.7287 |