Abstract
In this paper, the notions of integral 0 φ -stability of ordinary impulsive differential equations are introduced. The definition of integral 0 φ -stability depends significantly on the fixed time impulses. Sufficient conditions for integral 0 φ -stability are obtained by using comparison principle and piecewise continuous cone valued Lyapunov functions. A new comparison lemma, connecting the solutions of given impulsive differential system to the solution of a vector valued impulsive differential system is also established.
Highlights
Impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biological systems, industrial robotics, optimal control, bio-technology and so forth
To the best of our knowledge, the concept of integral stability and φ0 -stability were introduced for ordinary differential equations by Lakshmikantham in 1969 [1] and by Akpan in 1992 [2] respectively
In this paper, we introduce and establish integral φ0 -stability for impulsive ordinary differential equations:
Summary
Impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biological systems, industrial robotics, optimal control, bio-technology and so forth. Several types of stability have been defined and established in literature by academicians for impulsive ordinary differential equations. Various techniques such as scalar valued piecewise continuous Lyapunov functions, vector valued piecewise continuous Lyapunov functions, Rajumikhin method, comparison principle etc. This lemma plays an important role in establishing the main results of the paper. Sufficient conditions for integral φ0 -stability are obtained by employing comparison principle and piecewise continuous cone valued Lyapunov functions
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
