Schauder`s fixed-point theorem in approximate controllability problems - Babiarz, Artur; Klamka, Jerzy (1944- ); Niezabitowski, Michał (Zielona Góra: Uniwersytet Zielonogórski)
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