Abstract
We prove the existence of \(n\)-dimensional linear differential systems with the first approximation having all positive characteristic exponents, with exponentially decaying perturbations, and with exactly \(n-1 \) linearly independent solutions with negative Lyapunov exponents. Thus, in the linear case we obtain an anti-Perron version—a version opposite to the well-known Perron effect of changing the values of negative exponents of the linear approximation to positive ones for solutions of a differential system with a perturbation of higher-order smallness in a neighborhood of the origin and admissible growth outside it.
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Funding
This work was supported by the Belarussian (project no. F20P-005) and Russian (project no. 20-57-00001Bel_a) Foundations for Basic Research.
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Translated by V. Potapchouck
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Izobov, N.A., Il’in, A.V. On the Existence of Linear Differential Systems with All Positive Characteristic Exponents of the First Approximation and with Exponentially Decaying Perturbations and Solutions. Diff Equat 57, 1426–1433 (2021). https://doi.org/10.1134/S0012266121110021
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DOI: https://doi.org/10.1134/S0012266121110021