## Taiwanese Journal of Mathematics

### APPROXIMATE CONTROLLABILITY OF NONLINEAR DETERMINISTIC AND STOCHASTIC SYSTEMS WITH UNBOUNDED DELAY

#### Abstract

In this paper, we consider approximate controllability for nonlinear deterministic and stochastic systems with resolvent operators and unbounded delay. We study the problem of approximate controllability of deterministic nonlinear differential equations with impulsive terms, resolvent operators and unbounded delay. Next, approximate controllability results are being established for a class of nonlinear stochastic differential equations with resolvent operators in a real separable Hilbert spaces. By using the resolvent operators and fixed point technique, sufficient conditions have been formulated and proved. In this paper, we prove the approximate controllability of nonlinear deterministic and stochastic control systems under the assumption that the corresponding linear system is approximately controllable. Examples are presented to illustrate the utility and applicability of the proposed method.

#### Article information

Source
Taiwanese J. Math., Volume 14, Number 5 (2010), 1777-1797.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406016

Digital Object Identifier
doi:10.11650/twjm/1500406016

Mathematical Reviews number (MathSciNet)
MR2724133

Zentralblatt MATH identifier
1220.93011

#### Citation

Sakthivel, R.; Nieto, Juan J.; Mahmudov, N. I. APPROXIMATE CONTROLLABILITY OF NONLINEAR DETERMINISTIC AND STOCHASTIC SYSTEMS WITH UNBOUNDED DELAY. Taiwanese J. Math. 14 (2010), no. 5, 1777--1797. doi:10.11650/twjm/1500406016. https://projecteuclid.org/euclid.twjm/1500406016

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