Conditions of existence and uniqueness of solutions for set-valued Volterra integral equation
Journal Title: Дослідження в математиці і механіці - Year 2016, Vol 21, Issue 2
Abstract
In 1969, F. S. de Blasi and F. Iervolino examined set-valued differential equation (differential equation with derivative Hukuhara). In the future, many authors have studied the question of the existence, uniqueness and properties of set-valued solutions of differential and integraldifferential equations, higher-order equations, investigated the impulse and control systems, as well as the possibility of using the asymptotic methods (the averaging method) has been proved for such systems. In recent years, all of these studies were transformed into the theory of set-valued equations as an independent theory. As this theory is widely used in control theory, differential inclusions, fuzzy systems, and others. In this paper we proved the existence and uniqueness theorem for one of the types of set-valued Volterra integral equations.
Authors and Affiliations
T. A. Komleva, L. I. Plotnikova, A. V. Plotnikov
Keywords
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