Abstract
In this paper, we established the some sufficient conditions for controllability of impulsive functional integrodifferential equations with nonlocal conditions by using the measure of noncompactness and Monch fixed point theorem.
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 t x′ t = A t x t + f t, x t + t, s, x(s) ds
Many authors have been studied the control of nonlinear systems with and without impulses; see for instance[5, 6, 7]
U t, s : ∆= t, s ε 0, b × 0, b : 0 ≤ s ≤ t ≤ b → L X, differential evolution equations with nonlocal here, X is a Banach space, L X is the space of all conditions bounded linear operators in X;f: 0, b × X →
Summary
U t, s : ∆= t, s ε 0, b × 0, b : 0 ≤ s ≤ t ≤ b → L X , differential evolution equations with nonlocal here, X is a Banach space, L X is the space of all conditions bounded linear operators in X;f: 0, b × X → Sare impulsive functions; M: PC 0, b ; X → X; B is a bounded linear operators from a Banach space V to X and the control functionu(∙) is given in L2( 0, b , V).
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