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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 53

On the Method of Guiding Functions in the Problem of the Existence of Bounded Solutions for Differential Inclusions

Author(s)

Sergey V. Kornev1, Polina S. Korneva1, Valerii V. Obukhovskii1

1Voronezh State Pedagogical University, Voronezh, Russian Federation 

Abstract
At the end of the 20th — beginning of the 21st centuries, in connection with the new opportunity of applications to current problems of mathematics, mechanics, control theory, physics and other sciences, the need arose for a significant expansion of the classes of guiding functions under consideration, first introduced by M. A. Krasnosel’skii and A. I. Perov. In particular, for differential equations, a class of guiding functions on a given set and a class of multivalent vector guiding functions were introduced, which were later generalized to the case of differential inclusions. In this paper, along with the classical method of guiding functions, the method of guiding functions on a given set and the method of multivalent vector guiding functions are applied to the problem of the existence of bounded solutions in nonlinear objects described by differential inclusions, the right-hand side of which has convex compact values, satisfies the upper Caratheodory conditions and the sublinear growth condition.
About the Authors

Sergey V. Kornev, Dr. Sci. (Phys.–Math.), Assoc. Prof., Voronezh State Pedagogical University, Voronezh, 394043, Russian Federation, kornev vrn@rambler.ru 

Polina S. Korneva, Student, Voronezh State Pedagogical University, Voronezh, 394043, Russian Federation, polinakorneva03@mail.ru 

Valerii V. Obukhovskii, Dr. Sci. (Phys.–Math.), Prof., Voronezh State Pedagogical University, Voronezh, 394043, Russian Federation, valerio-ob2000@mail.ru

For citation
Kornev S. V., Korneva P. S., Obukhovskii V. V. On the Method of Guiding Functions in the Problem of the Existence of Bounded Solutions for Differential Inclusions. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 53, pp. 69–84. (in Russian) https://doi.org/10.26516/1997-7670.2025.53.69
Keywords
guiding function, bounded solution, differential inclusion, Caratheodory conditions
UDC
517.911.5
MSC
34A60, 34K09
DOI
https://doi.org/10.26516/1997-7670.2025.53.69
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Full text (russian)