Hyers–Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems

Akbar Zada, Omar Shah and Rahim Shah

Applied Mathematics and Computation, 2015, vol. 271, issue C, 512-518

Abstract: In this paper, the concepts of Hyers–Ulam stability are generalized for non-autonomous linear differential systems. We prove that the k-periodic linear differential matrix system Z˙(t)=A(t)Z(t),t∈R is Hyers–Ulam stable if and only if the matrix family L=E(k,0) has no eigenvalues on the unit circle, i.e. we study the Hyers–Ulam stability in terms of dichotomy of the differential matrix system Z˙(t)=A(t)Z(t),t∈R. Furthermore, we relate Hyers–Ulam stability of the system Z˙(t)=A(t)Z(t),t∈R to the boundedness of solution of the following Cauchy problem: {Y˙(t)=A(t)Y(t)+ρ(t),t≥0Y(0)=x−x0,where A(t) is a square matrix for any t∈R,ρ(t) is a bounded function and x,x0∈Cm.

Keywords: Non-autonomous Cauchy problem; Dichotomy; Hyers–Ulam stability (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:271:y:2015:i:c:p:512-518

DOI: 10.1016/j.amc.2015.09.040

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