Двухточечная краевая задача для системы функционально-дифференциальных уравнений с максимумами
Двухточечная краевая задача для системы функцио
DOI:
https://doi.org/10.56143/ujmcs.v1i2.7Ключевые слова:
Краевая задача, система обыкновенных дифференциальных уравнений, метод параметризации, необходимые и достаточные условия, существование и единственность решения.Аннотация
В данной статье рассматриваются вопросы краевой задачи с двухточечными граничными условиями для системы обыкновенных дифференциальных уравнений первого порядка с максимумами. Используется метод параметризации. Получены условия сходимости и построены алгоритмы решения. Установлены необходимые и достаточные условия на коэффициенты для корректности рассматриваемой задачи. В доказательстве однозначной разрешимости функционально-интегральных уравнений в пространстве $BD\big([0,\omega],\mathbb{R}^{n} \big)$ используется метод сжимающих отображений.
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