The ulam-hyers stability of an ordinary differential equation via gronwall lemmas

被引:0
作者
Petruşel A. [1 ,2 ]
Rus I.A. [1 ]
机构
[1] Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca
[2] Academy of Romanian Scientists, Bucharest
来源
Applied Set-Valued Analysis and Optimization | 2020年 / 2卷 / 03期
关键词
Cauchy problem; Differential equation; Gronwall lemma; Integral equation; Ulam-Hyers stability;
D O I
10.23952/asvao.2.2020.3.04
中图分类号
学科分类号
摘要
Following [I.A. Rus, Gronwall lemma approach to the Hyers-Ulam-Rassias stability of an integral equation, in: Nonlinear Analysis and Variational Problems, Panos Pardalos, Themistocles M. Rassias, Akhtar A. Khan (ed.), pp. 147-152, Springer, 2009], we study the Ulam-Hyers stability of some ordinary differential equations based on Gronwall lemmas. ©2020 Applied Set-Valued Analysis and Optimization
引用
收藏
页码:295 / 303
页数:8
相关论文
共 21 条
  • [1] Agarwal R.P., O'Regan D., Infinite Interval Problems for Differential, Difference and Integral Equations, (2001)
  • [2] Amann H., Ordinary Differential Equations, (1990)
  • [3] Bainov D., Simeonov P., Integral Inequalities and Applications, (1992)
  • [4] Coddington E.A., Levinson N., The Theory of Ordinary Differential Equations, (1955)
  • [5] Dieudonne J., Foundations of Modern Analysis, (1960)
  • [6] Gavruta P., Gavruta L., A new method for the generalized Hyers-Ulam-Rassias stability, Int. J. Nonlinear Anal. Appl, 1, pp. 11-18, (2010)
  • [7] Hartman P., Ordinary Differential Equations, (1964)
  • [8] Jung S.-M., A fixed point approach to the stability of a Volterra integral equation, Fixed Point Theory Appl, 2007, (2007)
  • [9] La Salle J.P., The Stability of Dynamical Systems, (1976)
  • [10] Petrusel A., Rus I.A., Ulam stability of zero point equations, Ulam Type Stability, pp. 345-364, (2019)