TY - JOUR

T1 - Existence of Two-Point Oscillatory Solutions of a Relay Nonautonomous System with Multiple Eigenvalue of a Real Symmetric Matrix

AU - Yevstafyeva, V. V.

N1 - Publisher Copyright: © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2021/12/1

Y1 - 2021/12/1

N2 - We study an n-dimensional system of ordinary differential equations with hysteresis type relay nonlinearity and a periodic perturbation function on the right-hand side. It is supposed that the matrix of the system is real and symmetric and, moreover, 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 time of return to each of these points. For these solutions, we prove the existence and nonexistence theorems. For a three-dimensional system, these results are illustrated by a numerical example.

AB - We study an n-dimensional system of ordinary differential equations with hysteresis type relay nonlinearity and a periodic perturbation function on the right-hand side. It is supposed that the matrix of the system is real and symmetric and, moreover, 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 time of return to each of these points. For these solutions, we prove the existence and nonexistence theorems. For a three-dimensional system, these results are illustrated by a numerical example.

UR - http://www.scopus.com/inward/record.url?scp=85120303403&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/90453a41-46b7-369a-ba6a-31bd09e1cbdf/

U2 - 10.1007/s11253-021-01957-4

DO - 10.1007/s11253-021-01957-4

M3 - Article

AN - SCOPUS:85120303403

VL - 73

SP - 746

EP - 757

JO - Ukrainian Mathematical Journal

JF - Ukrainian Mathematical Journal

SN - 0041-5995

IS - 5

ER -