NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEM FOR A SECOND ORDER IMPULSIVE SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS WITH MIXED MAXIMA: NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEM FOR A SECOND ORDER IMPULSIVE SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS WITH MIXED MAXIMA

Азиз Файзиев

doi:10.52754/16948645_2023_2_208

Авторы

Кудратиллаевич Ташкентский государственный экономический университет Ташкент, Узбекистан

DOI:

https://doi.org/10.52754/16948645_2023_2_208

Ключевые слова:

система второго порядка, импульсные интегро-дифференциальные уравнения, двухточечные нелинейные краевые условия, смешанные максимумы, последовательные приближения, существование и единственность решения

Аннотация

Исследуется двухточечная нелинейная краевая задача для системы обыкновенных интегро-дифференциальных уравнений второго порядка с импульсными эффектами и смешанными максимумами. Путем применения некоторых преобразований получается система нелинейных функциональных интегральных уравнений. Существование и единственность решения непериодической двухточечной краевой задачи сводятся к однозначной разрешимости системы нелинейных функциональных интегральных уравнений в Банаховом пространстве . Метод последовательных приближений в сочетании с методом сжимающих отображений используется при доказательстве однозначной разрешимости нелинейных функциональных интегральных уравнений.

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NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEM FOR A SECOND ORDER IMPULSIVE SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS WITH MIXED MAXIMA