Abstract
This paper proves the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of nonlinear first-order ordinary differential equation with single constant delay and finite impulses on a compact interval. Our approach uses abstract Gronwall lemma together with integral inequality of Gronwall type for piecewise continuous functions.
Highlights
Ulam, in [1], put a question regarding the stability of functional equation for homomorphism in front of a Mathematical Colloquium
This paper proves the Hyers-Ulam stability and the Hyers-Ulam-Rassias stability of nonlinear first-order ordinary differential equation with single constant delay and finite impulses on a compact interval
In [1], put a question regarding the stability of functional equation for homomorphism in front of a Mathematical Colloquium
Summary
In [1], put a question regarding the stability of functional equation for homomorphism in front of a Mathematical Colloquium. To study Hyers-Ulam stability of differential equations, different researchers presented their works with different approaches; for example, see [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. They, in 2012, obtained four Ulam’s type stability concepts for first-order nonlinear impulsive ordinary differential equation on closed bounded interval with finite impulses.
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