Abstract
In this paper, using Sadovskii’s fixed point theorem and properties of the measure of noncompactness, we obtain asymptotic stability results for solutions of nonlinear differential equation with variable delay. Results presented in this paper extend some previous results due to Burton [1], Becker and Burton [2], Ardjouni and Djoudi [3], and Jin and Luo [4].
Highlights
Since 1892, the Lyapunov’s direct method has been used for the study of stability properties of ordinary, functional, differential and partial differential equations
Sadovskii’s fixed point theorem and techniques of the theory of the measure of noncompactness are used to prove the existence and stability of the solution of the problem investigated in this paper
In [13], Burton and Furumochi using the fixed point theorem of Krasnosielski obtained boundedness and asymptotic stability for the equation: x′(t ) = −a (t ) x (t − r1 ) + b (t ) xγ (t − r2 (t )), where r1 > 0 is constant; γ ∈ (0,1) and γ is a quotient with odd positive
Summary
Since 1892, the Lyapunov’s direct method has been used for the study of stability properties of ordinary, functional, differential and partial differential equations. Sadovskii’s fixed point theorem (see [18]) and techniques of the theory of the measure of noncompactness are used to prove the existence and stability of the solution of the problem investigated in this paper. ( ) Here CB R+ , E denotes the set of all continuous and bounded functions f : R+ → E with the supremum norm ⋅ defined
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
