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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Multiperiodic solutions of quasilinear systems of integro-differential equations with $D_c$-operator and $\epsilon$-period of hereditarity
Zh. A. Sartabanov, G. M. Aitenova, G. A. Abdikalikova Department of Mathematics,
K. Zhubanov Aktobe Regional State University,
34 A. Moldagulova St,
030000 Aktobe, Kazakhstan
Аннотация:
We investigate a quasilinear system of partial integro-differential equations with the operator of differentiation in the direction of a vector field, which describes the process of hereditary propagation with an $\epsilon$-period of heredity. Under some conditions on the input data, conditions for the solvability of the initial problem for a quasilinear system of integro-differential equations are obtained. On this basis, sufficient conditions for the existence of multiperiodic solutions of integro-differential systems are found under the exponential dichotomy additional assumption on the corresponding homogeneous integro-differential system. The unique solvability of an operator equation in the space of smooth multiperiodic functions is proved, to which the main question under consideration reduces. Thus, sufficient conditions are established for the existence of a unique multiperiodical in all time variables solution of a quasilinear system of integro-differential equations with the differentiation operator in the directions of a vector field and a finite period of hereditarity.
Ключевые слова и фразы:
integro-differential equation, hereditarity period, quasilinear system, multiperiodic solution, differentiation operator, vector field.
Поступила в редакцию: 22.10.2019
Образец цитирования:
Zh. A. Sartabanov, G. M. Aitenova, G. A. Abdikalikova, “Multiperiodic solutions of quasilinear systems of integro-differential equations with $D_c$-operator and $\epsilon$-period of hereditarity”, Eurasian Math. J., 13:1 (2022), 86–100
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj433 https://www.mathnet.ru/rus/emj/v13/i1/p86
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Страница аннотации: | 114 | PDF полного текста: | 37 | Список литературы: | 16 |
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