Існування двоточково-коливальних розв’язків релейної неавтономної системи з кратним власним числом дійсної симетричної матриці

V. V. Yevstafyeva

doi:10.37863/umzh.v73i5.6379

V. V. Yevstafyeva Saint Petersburg State University

DOI: https://doi.org/10.37863/umzh.v73i5.6379

Abstract

UDC 517.925

We study an $n$-dimensional system of ordinary differential equations with a hysteresis type relay nonlinearity and a periodic perturbation function in the right-hand side.
It is supposed that the matrix of the system is real and symmetric and it has an eigenvalue of multiplicity two.
In the phase space of the system, we consider continuous bounded oscillatory solutions with two fixed points and the same return time to each of these points.
For such solutions, we prove the existence and nonexistence theorems.
These results are illustrated by a numerical example for a three-dimensional system.

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Existence of two-point oscillatory solutions of a relay nonautonomous system with a multiple eigenvalue of a real symmetric matrix

Abstract

References