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- W1860336393 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 ) + ? ( t ) , t ? 0 Y ( 0 ) = x - x 0 , where A(t) is a square matrix for any t ? R , ?(t) is a bounded function and x , x 0 ? C m ." @default.
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- W1860336393 date "2015-11-01" @default.
- W1860336393 modified "2023-09-25" @default.
- W1860336393 title "Hyers–Ulam stability of non-autonomous systems in terms of boundedness of Cauchy problems" @default.
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- W1860336393 doi "https://doi.org/10.1016/j.amc.2015.09.040" @default.
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