On Hyers–Ulam and Hyers–Ulam–Rassias Stability of a Nonlinear Second-Order Dynamic Equation on Time Scales
Abstract
:1. Introduction
2. Sufficient Conditions for Existence and Uniqueness of Solutions
- (A)
- and .
- (B)
- and h satisfy the Lipschitz conditions with constants and , respectively.
- (C)
- For any , (1) has a solution satisfying .
- (D)
- There is such that
3. Hyers–Ulam Stability Results
4. Hyers–Ulam–Rassias Stability
Author Contributions
Funding
Conflicts of Interest
Abbreviations
HUS | Hyers–Ulam stability |
HUSR | Hyers–Ulam–Rassias stability |
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Hamza, A.E.; Alghamdi, M.A.; Alharbi, M.S. On Hyers–Ulam and Hyers–Ulam–Rassias Stability of a Nonlinear Second-Order Dynamic Equation on Time Scales. Mathematics 2021, 9, 1507. https://doi.org/10.3390/math9131507
Hamza AE, Alghamdi MA, Alharbi MS. On Hyers–Ulam and Hyers–Ulam–Rassias Stability of a Nonlinear Second-Order Dynamic Equation on Time Scales. Mathematics. 2021; 9(13):1507. https://doi.org/10.3390/math9131507
Chicago/Turabian StyleHamza, Alaa E., Maryam A. Alghamdi, and Mymonah S. Alharbi. 2021. "On Hyers–Ulam and Hyers–Ulam–Rassias Stability of a Nonlinear Second-Order Dynamic Equation on Time Scales" Mathematics 9, no. 13: 1507. https://doi.org/10.3390/math9131507