Bounds for solutions of linear differential equations and Ulam stability

Blaga, F.; Mesaroş, Laura; Popa, Dorian; Pugna, Georgiana; Raşa, Ioan

doi:10.18514/mmn.2020.2903

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2022

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Cited by 4 publications

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“…The paper [7] established the Hyers-Ulam stability of a system of firstorder linear differential equations with constant coefficients, followed by [8,9]. Other recent papers on HUS and differential systems include [3,4]. In this work, we sharpen and clarify those results, in the 2 × 2 constant coefficient matrix case, by providing necessary and sufficient conditions for the linear system to be Hyers-Ulam stable, and we suss out specific Hyers-Ulam constants in the event of Hyers-Ulam stability, including specific cases with the minimal constant.…”

Section: Introductionmentioning

confidence: 99%

Hyers-Ulam stability for differential systems with $2\times 2$ constant coefficient matrix

Anderson¹,

Onitsuka²

2022

Preprint

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We explore the Hyers-Ulam stability of perturbations for a homogeneous linear differential system with 2 × 2 constant coefficient matrix. New necessary and sufficient conditions for the linear system to be Hyers-Ulam stable are proven, and for the first time, the best (minimal) Hyers-Ulam constant for systems is found in some cases. Several examples are provided. Obtaining the best Hyers-Ulam constant for second-order constant coefficient differential equations illustrates the applicability of the strong results.

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