We establish the Hyers-Ulam stability of a second-order linear Hill-type $h$-difference equation with a periodic coefficient. Using results from first-order $h$-difference equations with periodic coefficient of arbitrary order, both homogeneous and non-homogeneous, we also establish a Hyers-Ulam stability constant. Several interesting examples are provided. As a powerful application, we use the main result to prove the Hyers-Ulam stability of a certain third-order $h$-difference equation with periodic coefficients of one form.
Categories: math.CA