Generalized Hyers‐Ulam Stability of the Second‐Order Linear Differential Equations

Abstract

We prove the generalized Hyers-Ulam stability of the 2nd-order linear differential equation of the form , with condition that there exists a nonzero in such that and is an open interval. As a consequence of our main theorem, we prove the generalized Hyers-Ulam stability of several important well-known differential equations.

Hyers - Ulam Stability of First and Second Order Partial Differential Equations

“…Hyers Ulam (HU) stability of differential equation has drawn much attention since Ulam's [16] presentation of the problem on stability of group homomorphism in 1940 and Hyers' [5] partial solution to it in 1941. For ordinary differential equations one can refer [3,15,6,7] and [8,9] for partial differential equations. Its various extensions have been named with additional word.…”

Ulam Stability for a Class of Hill’s Equations

“…For example see the works of Li and Huang [14], Li and Shen [15], and Xue [16]. On the other hand, there are many studies on the second-order linear differential equations with variable coefficients (see, [17][18][19][20][21][22][23][24]). It is well known that the most commonly encountered variable coefficient second order differential equation is Hill's equation…”

Hyers-Ulam Stability of a Perturbed Generalised Lienard Equation

“…This phenomenon of the stability that was introduced by Rassias leads to Hyers-Ulam-Rassias stability (or the generalized Hyers-Ulam stability), see [8].…”