Ulam’s type stability of impulsive ordinary differential equations☆

By Jinrong Wang, Michal Fec˘kan, Yong Zhou. 2012

262 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/910096a0831d64cc8f0e07de6eae5d8382a1d9a1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Akbar Zada
2. Jinrong Wang
3. Mouffak Benchohra
4. S. Bouriah
5. Wajid Ali
6. Tongxing Li
7. Shah Faisal
8. Yong Zhou

In Modeling and Simulation

1. Akbar Zada
2. Jinrong Wang
3. Mouffak Benchohra
4. S. Bouriah
5. Wajid Ali
6. Tongxing Li
7. Yong Zhou
8. Donal O'Regan

Citations in the corpus

• Existence and Stability Results for Nonlinear Boundary Value Problem for Implicit Differential Equations of Fractional Order (2015, methodology): “For more detailed definitions of the Hyers-Ulam stability and the generalized Hyers-Ulam stability, we refer the reader to the papers [1, 7, 8, 14, 16, 19, 20, 22, 26, 29, 34, 35, 36] and the books [13, 27, 28].”
• On the Hyers-Ulam Stability of First-Order Impulsive Delay Differential Equations (2016, unknown): “Remark 6 (see [30]).”
• Existence and Hyers‐Ulam stability of fractional nonlinear impulsive switched coupled evolution equations (2018, unknown): “Now for any (p, q) ∈ E and t ∈ J, one can derive ||Υ1(p, q) − Υ1(?̄?, q̄)||PC ≤ κ1||p − ?̄?||PC + mL1||p − ?̄?||PC + mK1 T Γ(σ + 1) ||p − ?̄?||PC +K1 T Γ(σ + 1) ||p − ?̄?||PC +MΘ mT Γ(σ + 1) [||p − ?̄?||PC + ||q − q̄||PC] +MΘ T Γ(σ + 1) [||p − ?̄?||PC + ||q − q̄||PC], (24)”
• Stability of higher-order nonlinear impulsive differential equations (2016, methodology): “In recent years, Hyers–Ulam stability and Hyers–Ulam–Rassias stability of impulsive differential equations have always attracted interest of researchers; see, for instance, [3, 14, 19, 26, 27, 33].”
• Ulam’s-Type Stability of First-Order Impulsive Differential Equations with Variable Delay in Quasi–Banach Spaces (2018, methodology): “,m, is said to be Hyers–Ulam stable [1], if there exists a real number $>0 such that for each : > 0 and for each solution y ∈ PC1([0,T],R) of inequality { |y′(t) – f (t, y(t))| < :, t ∈ [0,T]\{t1, t2, .”