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Hyers–Ulam stability of linear differential equations of second order

✍ Scribed by Yongjin Li; Yan Shen

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
304 KB
Volume
23
Category
Article
ISSN
0893-9659

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✦ Synopsis

We prove the Hyers-Ulam stability of linear differential equations of second order. That is, if y is an approximate solution of the differential equation y + αy + βy = 0, then there exists an exact solution of the differential equation near to y.

📜 SIMILAR VOLUMES

Hyers–Ulam stability of linear different
Hyers–Ulam stability of linear differential operator with constant coefficients
✍ Takeshi Miura; Shizuo Miyajima; Sin–Ei Takahasi 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 132 KB

## Abstract Let __P__(__z__) be a polynomial of degree __n__ with complex coefficients and consider the __n__–th order linear differential operator __P__(__D__). We show that the equation __P__(__D__)__f__ = 0 has the Hyers–Ulam stability, if and only if the equation __P__(__z__) = 0 has no pure im

Hyers–Ulam stability of additive set-val
Hyers–Ulam stability of additive set-valued functional equations
✍ Gang Lu; Choonkil Park 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 213 KB

In this paper, we define the following additive set-valued functional equations (1) for some real numbers α > 0, β > 0, r, s ∈ R with α + β = r + s ̸ = 1, and prove the Hyers-Ulam stability of the above additive set-valued functional equations.