Hyers–Ulam stability of linear differential operator with constant coefficients

Let P ( z ) be a polynomial of degree n with complex coefficients and consider the n –th order linear differential operator P ( D ). We show that the equation P ( D ) f = 0 has the Hyers–Ulam stability, if and only if the equation P ( z ) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)