Best constant in Hyers-Ulam stability of first-order homogeneous linear differential equations with a periodic coefficient

This paper is concerned with Hyers-Ulam stability of the first-order homogeneous linear differential equation x' - a(t)x = 0 on R, where a : R -> R is a continuous periodic function. It is known that if a(t) = 0 then the above equation does not have Hyers-Ulam stability on R. However, sufficient conditions for Hyers-Ulam stability are presented in spite of a(t) has infinitely many zeros and changes sign. Furthermore, the best constant in Hyers-Ulam stability is clarified. To illustrate the obtained results, some examples are included. (C) 2019 The Author(s). Published by Elsevier Inc.