Best Constant in Ulam Stability for the Third Order Linear Differential Operator with Constant Coefficients

Abstract

The authors of the present paper previously proved the Ulam stability for the n-th-order linear differential operator with constant coefficients. They obtained its best Ulam constant for the case of distinct roots of the characteristic equation. However, a complete answer to the problem of the best Ulam constant was later obtained only for the second-order linear differential operator. This paper deals with the Ulam stability of the third-order linear differential operator with constant coefficients acting in a Banach space. The paper’s main purpose is to obtain the best Ulam constant of this operator, thus completing the previous research in the field.