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Эта публикация цитируется в 13 научных статьях (всего в 13 статьях)
New general solution to a nonlinear Fredholm integro-differential equation
D. S. Dzhumabaevab, S. T. Mynbayevabc a International Information Technology University,
34A Dzhandossov St,
050034 Almaty, Kazakhstan
b Institute of Mathematics and Mathematical Modeling MES RK,
125 Pushkin St,
050010 Almaty, Kazakhstan
c K. Zhubanov Aktobe Regional State University,
34 Moldagulova Av,
030000, Aktobe, Kazakhstan
Аннотация:
Partition $\Delta_N$ of the interval $[0, T]$ into $N$ parts and introduction of additional parameters and new unknown functions on subintervals reduce a nonlinear Fredholm integro-differential equation to the special Cauchy problems for a system of nonlinear integro-differential equations with parameters. Conditions for the existence of a unique solution to the latter problem are obtained. Employing this solution we construct a $\Delta_N$ general solution to the nonlinear Fredholm integro-differential equation. Properties of the $\Delta_N$ general solution and its application to a nonlinear boundary value problem for the considered equation are discussed.
Ключевые слова и фразы:
nonlinear Fredholm integro-differential equation, special Cauchy problem, $\Delta_N$ general solution, boundary value problem.
Поступила в редакцию: 06.09.2019
Образец цитирования:
D. S. Dzhumabaev, S. T. Mynbayeva, “New general solution to a nonlinear Fredholm integro-differential equation”, Eurasian Math. J., 10:4 (2019), 24–33
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/emj345 https://www.mathnet.ru/rus/emj/v10/i4/p24
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Страница аннотации: | 238 | PDF полного текста: | 115 | Список литературы: | 26 |
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