On Hyers-Ulam Stability of Nonlinear Differential Equations

Abstract

Abstract. We investigate the stability of nonlinear differential equations of the form y (n) (x) = F (x, y(x), y ′ (x), . . . , y (n−1) (x)) with a Lipschitz condition by using a fixed point method. Moreover, a Hyers-Ulam constant of this differential equation is obtained.

Analysis of Implicit Type Nonlinear Dynamical Problem of Impulsive Fractional Differential Equations

“…Later on, Hyers results are extended by many mathematicians; for details, reader may see [32][33][34][35][36][37][38][39] and the reference therein. The mentioned stability analysis is extremely helpful in numerous applications, for example, numerical analysis and optimization, where it is very tough to find the exact solution of a nonlinear problem.…”

Stability via successive approximation for nonlinear implicit fractional differential equations

“…Motivation and basic theoretical development for the research related to Ulam-Hyers stability and Ulam-Hyers-Rassias stability problems to various forms of ordinary differential and integral equations of integer orders can be found in [2,3,4,5,6,7,8,9,10] and the references given therein.…”

Hyers–Ulam stability of delay differential equations of first order

“…In recent years, accompanied by the development of the Hyers–Ulam stability (also called Ulam–Hyers stability) of functional equations, e.g. , , , , –, many mathematicians paid attention to the problem of differential equations, for the papers concerning ordinary differential equations we refer the readers to , , , –, , , , . Further, the interested readers can see , , , , concerning the Hyers–Ulam stability of partial differential equations.…”