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Paper details
Number 2 - June 2016
Volume 26 - 2016
Schauder’s fixed-point theorem in approximate controllability problems
Artur Babiarz, Jerzy Klamka, Michał Niezabitowski
Abstract
The main objective of this article is to present the state of the art concerning approximate controllability of dynamic systems
in infinite-dimensional spaces. The presented investigation focuses on obtaining sufficient conditions for approximate
controllability of various types of dynamic systems using Schauder’s fixed-point theorem. We describe the results of approximate controllability for nonlinear impulsive neutral fuzzy stochastic differential equations with nonlocal conditions,
impulsive neutral functional evolution integro-differential systems, stochastic impulsive systems with control-dependent
coefficients, nonlinear impulsive differential systems, and evolution systems with nonlocal conditions and semilinear evolution equation.
Keywords
approximate controllability, Banach space, Hilbert space, Schauder’s fixed-point theorem, infinite-dimensional space