Abstract
The paper is concerned with the controllability of impulsive functional integrodifferential equations with nonlocal conditions. Using the measure of noncompactness and Monch fixed point theorem, we establish some sufficient conditions for controllability and also our theorems extend some analogous results of (impulsive) control systems.
Highlights
Impulsive differential equations are a class of important models which describes many evolution process that abruptly change their state at a certain moment,see the monographs of Bainov and Simonov (1993), Lakshmikantham et al (1989) and have been studied extensively by many authors (Cuevas et al, 2009; Fan and Li, 2010; Anguraj and Mallika Arjunan, 2009)
The starting point of this paper is the work in papers (Ji et al, 2011; Jose et al, 2013)
Motivated by above mentioned works (Ji et al, 2011; Jose et al, 2013), the main work of this paper is to prove the controllability results of impulsive integrodifferential systems with nonlocal conditions
Summary
Impulsive differential equations are a class of important models which describes many evolution process that abruptly change their state at a certain moment,see the monographs of Bainov and Simonov (1993), Lakshmikantham et al (1989) and have been studied extensively by many authors (Cuevas et al, 2009; Fan and Li, 2010; Anguraj and Mallika Arjunan, 2009). (2) β(Ω ∪ Ω ) ≤ max{β(Ω ) , β(Ω ) }; (3) β(λΩ) ≤ λ β Ω for any λε R; (4) If the map Q: D(Q) ⊆ X Z is Lipschitz continuous with constants k, βZ(QZ) ≤ kβ(Ω) for any bounded subset Ω ⊂ D(Q), where Z is a Banach space.
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