Hyers--Ulam stability of nth order linear differential equations

Hyers-ulam stability of exact second-order linear differential equations

* Correspondence: baak@hanyang. ac.kr Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea Full list of author information is available at the end of the article Abstract In this article, we prove the Hyers-Ulam stability of exact second-order linear differential equations. As a consequence, we show the Hyers-Ulam stability of the fo...

Hyers–ulam Stability of Linear Differential Equations with Vanishing Coefficients

We establish the Hyers-Ulam stability of certain first-order linear differential equations where the coefficients are allowed to vanish. We then extend these results to higher-order linear differential equations with vanishing coefficients that can be written with these first-order factors. AMS (MOS) Subject Classification. 34A30, 34A05, 34D20.

Hyers-Ulam stability of linear partial differential equations of first order

In this work, we will prove the Hyers–Ulam stability of linear partial differential equations of first order.

Hyers-Ulam Stability of Nonhomogeneous Linear Differential Equations of Second Order

Hyers-Ulam stability of first-order homogeneous linear differential equations with a real-valued coefficient

This paper is concerned with the Hyers–Ulam stability of the first-order linear differential equation x′ − ax = 0, where a is a non-zero real number. The main purpose is to find an explicit solution x(t) of x′−ax = 0 satisfying |φ(t)−x(t)| ≤ ε/|a| for all t ∈ R under the assumption that a differentiable function φ(t) satisfies |φ′(t)− aφ(t)| ≤ ε for all t ∈ R. In addition, the precise behavior ...