Best constant in Hyers-Ulam stability of first-order homogeneous linear differential equations with a periodic coefficient (Q2633363)

Sufficient conditions for Hyers-Ulam stability are established for the first-order homogeneous linear differential equation \[x'-a(t)x=0,\] where \(a(t)\) is a continuous periodic function. Results ae derived for the case when \(a(t)\) has infinitely many zeros and changes sign. The case \(a(t)=0\) does not possess Hyers-Ulam stability. Moreover, the authors clarify the best constant of the Hyers-Ulam stability. Numerical examples are given to illustrate the effectiveness and usefulness of the results.