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We consider a problem with periodic conditions in the time coordinate and conditions of 2$\pi$-periodicity in space variables for an n-th order equation that is not solvable with respect to the highest time derivative. The solvability of the problem is related to the problem of small denominators. T...
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| Date: | 2021 |
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| Main Author: | |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine
2021
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| Subjects: | |
| Online Access: | http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/apmm2021.19.57-62 |
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| Journal Title: | Prykladni Problemy Mekhaniky i Matematyky |
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Prykladni Problemy Mekhaniky i Matematyky| Summary: | We consider a problem with periodic conditions in the time coordinate and conditions of 2$\pi$-periodicity in space variables for an n-th order equation that is not solvable with respect to the highest time derivative. The solvability of the problem is related to the problem of small denominators. The paper considers the question of the existence and uniqueness of a solution to the problem, constructs an explicit formula for the solution in the form of a series in a system of orthogonal functions, and performs a metric analysis of lower bounds for small denominators that arise in constructing the solution. Cite as: L. I. Komarnytska, “Periodic problem for Sobolev type equation,” Prykl. Probl. Mekh. Mat., Issue 19, 57–62 (2021) (in Ukrainian), https://doi.org/10.15407/apmm2021.19.57-62 |
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