Viable solutions for second order nonconvex functional differential inclusions.
Viable solutions of differential inclusions with memory in Banach spaces.
Viral infection model with diffusion and state-dependent delay: a case of logistic growth
We propose a virus dynamics model with reaction-diffusion and logistic growth terms, intracellular state-dependent delay and a general non-linear infection rate functional response. Classical solutions with Lipschitz in-time initial functions are investigated. This type of solutions is adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions approach is used to analyse stability of interior infection equilibria which describe the cases of...
Viral in-host infection model with two state-dependent delays: stability of continuous solutions
A virus dynamics model with two state-dependent delays and logistic growth term is investigated. A general class of nonlinear incidence rates is considered. The model describes the in-host interplay between viral infection and CTL (cytotoxic T lymphocytes) and antibody immune responses. The wellposedness of the model proposed and Lyapunov stability properties of interior infection equilibria which describe the cases of a chronic disease are studied. We choose a space of merely continuous initial...
Visualisation of the electromagnetic vector fields
Modern computer algebra software can be used to visualize vector fields. One of the most used is the Maple program. This program is used to visualize two and three-dimensional vector fields. The possibilities of plotting direction vectors, lines of force, equipotential curves and the method of colouring the surface area for two-dimensional cases are shown step by step. For three-dimensional arrays, these methods are applied to various slices of three-dimensional space, such as a plane or a cylindrical...
Weighted fractional differential equations with infinite delay in Banach spaces
This paper is devoted to the study of fractional differential equations with Riemann-Liouville fractional derivatives and infinite delay in Banach spaces. The weighted delay is developed to deal with the case of non-zero initial value, which leads to the unboundedness of the solutions. Existence and uniqueness results are obtained based on the theory of measure of non-compactness, Schaude’s and Banach’s fixed point theorems. As auxiliary results, a fractional Gronwall type inequality is proved,...
Weighted pseudo almost automorphic functions with applications to abstract dynamic equations on time scales
We propose a concept of weighted pseudo almost automorphic functions on almost periodic time scales and study some important properties of weighted pseudo almost automorphic functions on almost periodic time scales. As applications, we obtain the conditions for the existence of weighted pseudo almost automorphic mild solutions to a class of semilinear dynamic equations on almost periodic time scales.
Weighted pseudo almost periodic solutions for functional differential equations.
Weighted pseudo-almost periodic solutions for some neutral partial functional differential equations.
Асимптотическая устойчивость системы дифференциальных уравнений с последействием, содержащих малый параметр
Базисность семейства решений Флоке линейного периодического уравнения нейтрального типа в гильбертовом пространстве.
Бифуркационные особенности сингулярно возмущенного уравнения с запаздыванием.
Дифференциальное чравнение с западывающим аргументом асимптотически эквивалентное с уравнением = 0
Достаточные условия положительности функции Коши и ее производных для дифференциального уравнения с запаздывающим аргументом
Достаточные условия существования решений Флоке уравнений нейтрального типа
Задача Kоши для одного класса полулинейных уравнений типа Соболева.
Заметка о колебломости решений дифференциальных уравнений второго порядкка с запаздывающим аргументом
К теории канонических форм систем управления с запаздыванием
Краевая задача для функционально-дифференциальных уравнений нейтрального типа
Краевая задача с параметрами для дифференциальных уравнений сверхнейтрального типа