Schauder's fixed-point theorem in approximate controllability problems

Artur Babiarz; Jerzy Klamka; Michał Niezabitowski

doi:10.1515/amcs-2016-0018

Schauder's fixed-point theorem in approximate controllability problems

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Abstrakt

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.

Język oryginału	angielski
Strony (od–do)	263-275
Liczba stron	13
Czasopismo	International Journal of Applied Mathematics and Computer Science
Tom	26
Numer wydania	2
Identyfikatory DOI	https://doi.org/10.1515/amcs-2016-0018
Status publikacji	Opublikowano - 1 cze 2016

Obszary tematyczne ASJC Scopus

Informatyka (różne)
Inżynieria (różne)
Matematyka stosowana

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10.1515/amcs-2016-0018

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keywords = "Banach space, Hilbert space, Schauder's fixed-point theorem, approximate controllability, infinite-dimensional space.",

author = "Artur Babiarz and Jerzy Klamka and Micha{\l} Niezabitowski",

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year = "2016",

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doi = "10.1515/amcs-2016-0018",

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AU - Babiarz, Artur

AU - Klamka, Jerzy

AU - Niezabitowski, Michał

PY - 2016/6/1

Y1 - 2016/6/1

N2 - 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.

AB - 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.

KW - Banach space

KW - Hilbert space

KW - Schauder's fixed-point theorem

KW - approximate controllability

KW - infinite-dimensional space.

UR - https://www.scopus.com/pages/publications/84978410149

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DO - 10.1515/amcs-2016-0018

M3 - Article

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JO - International Journal of Applied Mathematics and Computer Science

JF - International Journal of Applied Mathematics and Computer Science

IS - 2

ER -

Schauder's fixed-point theorem in approximate controllability problems

Abstrakt

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