A kind of stricter Hyers–Ulam stability of second order linear differential equations of Carathéodory type. (May 2021) - Yang, Yue; Meng, Fanwei
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 .