A kind of stricter Hyers–Ulam stability of second order linear differential equations of Carathéodory type. (May 2021)

• Record Type: Journal Article
• Authors: Yang, Yue; Meng, Fanwei
• Is Part Of: Applied mathematics letters. Volume 115(2021)
• Publication Date: 2021-05
• Subjects: Stricter Hyers–Ulam stability -- Linear differential equation -- Carathéodory type; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.106946
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: The purpose of this article is to establish a kind of stricter Hyers–Ulam stability of second order linear differential equation of Carathéodory type. More explicitly, we prove that if x is an approximate solution satisfying a kind of stricter condition of the differential equation x ′ ′ ( t ) + b 1 x ′ ( t ) + b 0 x ( t ) = f ( t ) without the assumption of continuity of f ( t ), then there exists an exact solution of the differential equation near to x .