Applied mathematics

Razumikhin approach in the generalized Myshkis problem for systems with distributed delay

A. V. Egorov

St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

Abstract: The paper gives sufficient conditions for the solvability of the generalized Myshkis problem for a system of equations with a distributed time-varying delay and a constant kernel. Conditions on the kernel which guarantee the uniform stability of the system for any admissible delay are obtained. The admissible delay in this paper is a piecewise continuous function bounded from above in magnitude and growth rate. The applicability of the obtained conditions is illustrated by two examples.

Keywords: time-delay system, stability, distributed delay, generalized Myshkis problem, Razumikhin approach.

UDC: 517.929

MSC: 93D09

Received: March 20, 2023
Accepted: April 25, 2023

DOI: 10.21638/11701/spbu10.2023.202