Periodic solutions for an impulsive system of integro-differential equations with maxima

Abstract

Исследуется краевая задача для системы обыкновенных интегро-дифференциальных уравнений первого порядка с импульсными эффектами и максимумами. Получена система нелинейных функционально-интегральных уравнений и, таким образом, существование и единственность решения периодической краевой задачи сводятся к разрешимости системы нелинейных функционально-интегральных уравнений. Метод последовательных приближений в сочетании его с методом сжимающих отображений используется при доказательстве однозначной разрешимости нелинейных функционально-интегральных уравнений. Определим способ, с помощью которого можно будет доказать существование периодических решений данной периодической краевой задачи.

Nonlinear Two-Point Boundary Value Problem for a Second Order Impulsive System of Integro-Differential Equations With Mixed Maxima

“…[0, ], n PC T R and taking into account estimates ( 16), (17), we conclude that the operator J has a unique fixed point.…”

“…Such differential and integro-differential equations are called equations with impulsive effects. A lot of publications of studying on differential and integro differential equations with impulsive effects, describing many natural and technical processes, are appearing (see, for examples, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Two-point and multi-point boundary value problems for the differential and integro-differential equations are studied by many authors (see, for example [21][22][23][24].…”

Mixed problem for a linear differential equation of parabolic type with nonlinear impulsive conditions

“…A lot of publications are devoted to study differential equations with impulsive effects, describing many natural and technical processes (see, for example, [39][40][41][42][43][44][45][46][47][48][49][50]). The questions of existence and uniqueness of periodic solutions of differential and integro-differential equations were studied in [51][52][53][54][55]. In [56][57][58], the Whitham type partial differential equations of the first order with impulsive effects are studied.…”

Determination of the coefficient function in a Whitham type nonlinear differential equation with impulse effects

“…In particular, such kind of problems appears in biophysics at micro-and nanoscales [6][7][8][9][10]. A lot of publications of studying the differential equations with impulse effects related to various natural and technical processes are appearing [11][12][13][14][15][16][17][18][19][20].…”