Abstract In this paper we give a characterization of Ulam stability for the linear partial differential operator D: C^1 (R^2, X) C (R^2, X) D: C 1 (R 2, X) → C (R 2, X) given by Du=auₗ+buₘ+cu D u = a u x + b u y + c u, where a, b, c R a, b, c ∈ R and X is a Banach space over R R. Moreover, we obtain the best Ulam constant of the operator D.
Novac et al. (Mon,) studied this question.