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Bull. Korean Math. Soc. 2015; 52(2): 685-697

Printed March 31, 2015

https://doi.org/10.4134/BKMS.2015.52.2.685

Copyright © The Korean Mathematical Society.

On Hyers-Ulam stability of nonlinear differential equations

Jinghao Huang, Soon-Mo Jung, and Yongjin Li

Sun Yat-Sen University, Hongik University, Sun Yat-Sen University

Abstract

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We investigate the stability of nonlinear differential equations of the form $y^{(n)}(x) = F(x, y(x), y'(x), \ldots, y^{(n-1)}(x))$ with a Lipschitz condition by using a fixed point method. Moreover, a Hyers-Ulam constant of this differential equation is obtained.

Keywords: Hyers-Ulam stability, generalized Hyers-Ulam stability, nonlinear differential equations, fixed point theorem

MSC numbers: 34D20, 26D10

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