Approximate controllability of semilinear functional equations in Hilbert spaces

Dauer, Jerald P.; Mahmudov, Nazım I.

doi:10.1016/s0022-247x(02)00225-1

Cited by 113 publications

(43 citation statements)

References 17 publications

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“…In the work of Dauer and Mahmudov (2002), the problem of approximate controllability of dynamic systems given by the following semilinear evolution equation is studied:…”

Section: Semilinear Functional Equationsmentioning

confidence: 99%

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Schauder’s fixed-point theorem in approximate controllability problems

Babiarz

Klamka

Niezabitowski

2016

International Journal of Applied Mathematics and Computer Science

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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.

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“…In the work of Dauer and Mahmudov (2002), the problem of approximate controllability of dynamic systems given by the following semilinear evolution equation is studied:…”

Section: Semilinear Functional Equationsmentioning

confidence: 99%

“…Babiarz et al point theorem was used by Dauer and Mahmudov (2002) in relation to approximate controllability of first order functional differential equations with finite delay. Approximate controllability of backward stochastic evolution equations in Hilbert space is considered by Dauer et al (2006).…”

mentioning

confidence: 99%

Schauder’s fixed-point theorem in approximate controllability problems

Babiarz

Klamka

Niezabitowski

2016

International Journal of Applied Mathematics and Computer Science

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“…We say that the system (SE) is approximate controllable on [0, T ] if for every desired final state x 1 and > 0 there exists a control function u ∈ L 2 (0, T ; U ) such that ||x(T ; f, u) − x 1 || H < . Dauer and Mahmudov [2] dealt with the approximate controllability of a semilinear control system as a particular case of sufficient conditions for approximate solvability of semilinear equations by assuming S(t) is compact operator for each t > 0, f is continuous and uniformly bounded and (1) the corresponding linear system (SE) when f ≡ 0 is approximately controllable.…”

Section: K(t − S)g(s X(s) U(s))dsmentioning

confidence: 99%

Controllability for Semilinear Functional Integrodifferential Equations

Jeong¹,

Kim²

2009

Bulletin of the Korean Mathematical Society

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Abstract. This paper deals with the regularity properties for a class of semilinear integrodifferential functional differential equations. It is shown the relation between the reachable set of the semilinear system and that of its corresponding linear system. We also show that the Lipschitz continuity and the uniform boundedness of the nonlinear term can be considerably weakened. Finally, a simple example to which our main result can be applied is given.

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“…(see [6,7,8] and references therein). The controllability of an abstract semilinear control system in infinite dimensional spaces is an important property and has been studied by many authors in recent past via functional analysis approach, see [9,10,11,12,13]. For the sake of brevity, we shall write V and Z for the spaces L 2 (0, 2π) and ω(x, t)dx is conserved, and in order to conserve this quantity, we define the bounded linear operator G on Z as…”

Section: Introductionmentioning

confidence: 99%