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

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...

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Bibliographic Details
Published in:Ukrainian mathematical journal 2021-10, Vol.73 (5), p.746-757
Main Author: Yevstafyeva, V. V.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Differential equations
Eigenvalues
Existence theorems
Fixed points (mathematics)
Geometry
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Ordinary differential equations
Periodic variations
Perturbation
Relay
Statistics
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Summary: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.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-021-01957-4