Controllability of nonlinear Itô type stochastic integrodifferential systems

Balachandran, K.; Karthikeyan, S.

doi:10.1016/j.jfranklin.2007.11.002

Cited by 22 publications

(10 citation statements)

References 20 publications

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“…The deterministic version of integro-differential systems have been thoroughly investigated (see Dhage and Graef (2010), Hernández (2004), Liang and Xiao (2004), Mohsen and El-Gamel (2010), Park, Balachandtran, and Annapoorani (2004) and references therein) while the stochastic version has been in growing state. In fact, existence results of mild solutions of stochastic integro-differential equations have been considered in Balachandran and Karthikeyan (2008), Balasubramaniam and Vinayagam (2005), Lin, Ren, and Xia (2010) and references therein. Byszewski and Lakshmikantham (1990) introduced nonlocal initial conditions into the initial-value problems and argued that the corresponding models more accurately described the phenomena.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Cauchy problem for some stochastic integro-differential equations in Hilbert spaces

Cui

Yan

2012

Journal of the Korean Statistical Society

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a b s t r a c tIn this paper, we study the existence results of mild solutions for a class of stochastic integro-differential equations with nonlocal conditions and stochastic impulsive integrodifferential equations with nonlocal conditions in Hilbert spaces. Sufficient conditions for the existence of mild solutions are derived by means of Leray-Schauder nonlinear alternative. An example is provided to illustrate the theory.

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Section: Introductionmentioning

confidence: 99%

Nonlocal Cauchy problem for some stochastic integro-differential equations in Hilbert spaces

Cui

Yan

2012

Journal of the Korean Statistical Society

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“…Controllability of nonlinear stochastic differential systems were discussed in [30][31][32][33][34][35][36][37]. Controllability of linear stochastic systems in finite-dimensional spaces is studied in [38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Banach fixed-point theorem in semilinear controllability problems – a survey

Klamka

Babiarz

Niezabitowski

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The main aim of this article is to review the existing state of art concerning the complete controllability of semilinear dynamical systems. The study focus on obtaining the sufficient conditions for the complete controllability for various systems using the Banach fixedpoint theorem. We describe the results for stochastic semilinear functional integro-differential system, stochastic partial differential equations with finite delays, semilinear functional equations, a stochastic semilinear system, a impulsive stochastic integro-differential system, semilinear stochastic impulsive systems, an impulsive neutral functional evolution integro-differential system and a nonlinear stochastic neutral impulsive system. Finally, two examples are presented.

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“…Over the past decades, stochastic systems have received much attention and many results have been reported [1,6,13,15,21,22]. Sufficiency conditions of complete controllability are established in [1] for nonlinear Itô stochastic integro-differential systems.…”

Section: Introductionmentioning

confidence: 99%

“…Sufficiency conditions of complete controllability are established in [1] for nonlinear Itô stochastic integro-differential systems. The robust stability and performance of stochastic uncertain systems over an infinite horizon are considered in [18], and the uncertainties of the systems are assumed to satisfy some relative entropy constraints.…”

Section: Introductionmentioning

confidence: 99%