Abstract
In this paper, Ulam’s-type stabilities are studied for a class of first-order impulsive differential equations with bounded variable delays on compact interval with finite number of impulses. Results of stability are proved via newly established integral inequality of Bellman–Grönwall–Bihari type with delay for discontinuous functions. Using this inequality for the first time and assumption of
Funding statement: This work was partially supported by Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006) and Science and Technology Program of Guizhou Province(Grant Number: [2017]5788).
References
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Articles in the same Issue
- Frontmatter
- Asymptotic Behavior of a Stochastic Two-Species Competition System with Impulsive Effects
- Flow Modeling of Well Test Analysis for a Multiple-fractured Horizontal Well in Triple Media Carbonate Reservoir
- Finite Element Analysis of Flexible Structure and Cavitating Nonlinear Acoustic Fluid Interaction under Shock Wave Loading
- On the Uniqueness of p-Best Approximation in Probabilistic Normed Spaces
- Existence of Mild Solutions for Sobolev-Type Hilfer Fractional Nonautonomous Evolution Equations with Delay
- On a Non-linear Boundary-Layer Problem for the Fractional Blasius-Type Equation
- Measurement and Control of Non-Linear Data Using ARMA Based Artificial Neural Network
- Pseudo Almost Periodicity and Its Applications to Impulsive Nonautonomous Partial Functional Stochastic Evolution Equations
- Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Difference Systems
- Existence and Multiple Solutions for Higher Order Difference Dirichlet Boundary Value Problems
- Compressive Wave Propagation in Highly Ordered Granular Media Based on DEM
- Ulam’s-Type Stability of First-Order Impulsive Differential Equations with Variable Delay in Quasi–Banach Spaces
Articles in the same Issue
- Frontmatter
- Asymptotic Behavior of a Stochastic Two-Species Competition System with Impulsive Effects
- Flow Modeling of Well Test Analysis for a Multiple-fractured Horizontal Well in Triple Media Carbonate Reservoir
- Finite Element Analysis of Flexible Structure and Cavitating Nonlinear Acoustic Fluid Interaction under Shock Wave Loading
- On the Uniqueness of p-Best Approximation in Probabilistic Normed Spaces
- Existence of Mild Solutions for Sobolev-Type Hilfer Fractional Nonautonomous Evolution Equations with Delay
- On a Non-linear Boundary-Layer Problem for the Fractional Blasius-Type Equation
- Measurement and Control of Non-Linear Data Using ARMA Based Artificial Neural Network
- Pseudo Almost Periodicity and Its Applications to Impulsive Nonautonomous Partial Functional Stochastic Evolution Equations
- Existence of Solutions to Boundary Value Problems for a Class of Nonlinear Difference Systems
- Existence and Multiple Solutions for Higher Order Difference Dirichlet Boundary Value Problems
- Compressive Wave Propagation in Highly Ordered Granular Media Based on DEM
- Ulam’s-Type Stability of First-Order Impulsive Differential Equations with Variable Delay in Quasi–Banach Spaces