HYERS-ULAM STABILITY OF SECOND-ORDER LINEAR DYNAMIC EQUATIONS ON TIME SCALES

doi:10.1007/s10473-021-0525-2

Abstract

Abstract: We investigate the Hyers-Ulam stability (HUS) of certain second-order linear constant coefficient dynamic equations on time scales, building on recent results for first-order constant coefficient time-scale equations. In particular, for the case where the roots of the characteristic equation are non-zero real numbers that are positively regressive on the time scale, we establish that the best HUS constant in this case is the reciprocal of the absolute product of these two roots. Conditions for instability are also given.

Key words: stability, second order, Hyers-Ulam, time scales

CLC Number:

34N05

Douglas R. ANDERSON, Masakazu ONITSUKA. HYERS-ULAM STABILITY OF SECOND-ORDER LINEAR DYNAMIC EQUATIONS ON TIME SCALES[J].Acta mathematica scientia,Series B, 2021, 41(5): 1809-1826.

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