Ulam stabilities of ordinary differential equations in a Banach space

Ioan A. Rus



Let (B, | · |) be a Banach space, A : B → B be the infinitesimal generator of a C0-semigroup, I := [a, b] or [a, +∞[ and f ∈ C(I × B, B). In this paper we present and discuss four types of Ulam stability: Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for the following differential equation u 0 (t) = A(u(t)) + f(t, u(t)), t ∈ I.

Additional Information


Rus Ioan A.