On Hyers-Ulam stability of nonlinear differential equations
Bull. Korean Math. Soc. 2015 Vol. 52, No. 2, 685-697
https://doi.org/10.4134/BKMS.2015.52.2.685
Published online March 31, 2015
Jinghao Huang, Soon-Mo Jung, and Yongjin Li
Sun Yat-Sen University, Hongik University, Sun Yat-Sen University
Abstract : 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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