Myslo Y. Asymptotically almost periodic solutions of differential equations with delay and impulses

The thesis is devoted to the study of piecewise continuous asymptotically almost periodic, almost periodic and periodic solutions for systems of differential equations with delay and impulsive action in fixed and non-fixed moments of time. The obtained results are used to find the conditions of existence and stability of positive piecewise continuous almost periodic solutions of the Mackey – Glass impulse equation and the model of the biological population with age structure and impulse action. The conditions for the existence of piecewise continuous asymptotically almost periodic and almost periodic solutions of systems with delays and unfixed moments of impulse action are found. The conditions for the existence and stability of positive piecewise continuous almost periodic solutions of the pulse logistics equation with delay and with non-fixed moments of pulse action are found. The conditions of permanence of the periodic system "predator-prey" with the age structure of the prey and impulse action, as well as the conditions of permanence and existence of positive asymptotically stable periodic solutions of the impulse system of delayed equations, which simulates the dynamics of two competing species with age structure.