Әдебиеттер
Jackson H.F. q-Difference equations, Am. J. Math. 32, (1910) 305-314.
Carmichael R.D., The general theory of linear q-difference equations,
Am. J. Math. 34 (1912) 147-168.
Kufner A., Maligranda L. and Persson L-E. The Hardy Inequality. About its History and Some Related Results, Vydavatelský Servis, Plzen, 2007, 162 pp.
УДК 517.91
О ФУРЬЕ ПРЕДСТАВЛЕНИИ СИЛЬНОГО РЕШЕНИЯ ЗАДАЧИ КОШИ ДЛЯ УРАВНЕНИЯ ШТУРМА-ЛИУВИЛЛЯ
Бердикулова М.К.
Южно-Казахстанский Государственный Университет им.М.О.Ауезова, г.Шымкент
Научный руководитель – д.ф.-м.н., доцент Шалданбаев А.Ш.
1.Постановка задачи. Пусть ![](data:image/png;base64,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) непрерывная функция на сегменте [0,1], т.е. ![](data:image/png;base64,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) . Рассмотрим задачу Коши для простейшего уравнения Штурма-Лиувилля:
![](data:image/png;base64,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) (1.1)
![](data:image/png;base64,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) (1.2)
ОПРЕДЕЛЕНИЕ 1.1. Регулярным решением краевой задачи (1.1)-(1.2) называется дважды непрерывно дифференцируемая функция ![](data:image/png;base64,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) , удовлетворяющая уравнения (1.1) и краевым условиям (1.2).
Для любой непрерывной функции ![](data:image/png;base64,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) существует единственное регулярное решение краевой задачи (1.1)-(1.2), которое задается формулой
![](data:image/png;base64,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) (1.3)
ОПРЕДЕЛЕНИЕ 1.2. Функция ![](data:image/png;base64,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) называется сильным решением задачи Коши (1.1)-(1.2), если существует последовательность регулярных решений ![](data:image/png;base64,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) задач Коши (1.1)-(1.2) такая, что ![](data:image/png;base64,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) в пространстве ![](data:image/png;base64,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) .
Достарыңызбен бөлісу: |