Hyers–Ulam Stability of a Class Second Differential Equation $$y''(x)+p(x)y'(x)+q(x)y(x)=F(y(x))$$ y ′ ′ ( x ) + p ( x ) y ′ ( x ) + q ( x ) y ( x ) = F ( y ( x ) )

Abstract

In this paper, we study the Hyers–Ulam–Rassias stability and Hyers–Ulam stability for a class second differential equation $$\begin{aligned} y''(x)+p(x)y'(x)+q(x)y(x)=F(y(x)) \end{aligned}$$ by a generalized fixed point theorem. Moreover, we show that the differential equation $$\begin{aligned} y'(x)=F(x,y(x)) \end{aligned}$$ has not the Hyers–Ulam stability on an infinite interval.