Instability of second-order nonhomogeneous linear difference equations with real-valued coefficients

In J. Comput. Anal. Appl. (2020), pp. 152–165, the author dealt with Hyers–Ulam stability of the second-order linear difference equation on , where and for the step size ; and are real numbers; is a real-valued function on . The purpose of this paper is to clarify that the second-order linear difference equation has no Hyers–Ulam stability when the step size and the coefficients and satisfy suitable conditions. Finally, a necessary and sufficient condition for Hyers–Ulam stability is obtained.