E. Z. Zainullina, V. S. Pavlenko, A. N. Sesekin, N. V. Gredasova, “On Ulam–Hyers stability of solutions to first-order differential equations with generalized action”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2022, Volume 209,Pages <nobr>25

On Ulam–Hyers stability of solutions to first-order differential equations with generalized action

E. Z. Zainullina^a, V. S. Pavlenko^a, A. N. Sesekin^ab, N. V. Gredasova^a

^a Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
^b N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg

Abstract: This paper is devoted to sufficient conditions for the Ulam–Hyers stability of solutions of first-order linear differential equations. We introduce the concept of the Ulam–Hyers stability for equations with unbounded right-hand sides whose solutions are functions of bounded variation and obtain sufficient conditions that guarantee this stability.

Keywords: Ulam–Hyers stability, differential equation, discontinuous solution.

UDC: 517.9

MSC: 34A37

DOI: 10.36535/0233-6723-2022-209-25-32