Controllability of nonlocal impulsive functional integrodifferential evolution systems
-
1732
Downloads
-
2598
Views
Authors
B. Radhakrishnan
- Department of Mathematics, Bharathiar University, Coimbatore, Tamil nadu, India.
K. Balachandran
- Department of Mathematics, Bharathiar University, Coimbatore, Tamil nadu, India.
Abstract
In this paper, we establish a set of sufficient conditions for the controllability
of nonlocal impulsive functional integrodifferential evolution systems with finite delay. The
controllability results are obtained with out assuming the compactness condition on the
evolution operator by using the semigroup theory and applying the fixed point approach.
An example is provided to illustrate the theory.
Share and Cite
ISRP Style
B. Radhakrishnan, K. Balachandran, Controllability of nonlocal impulsive functional integrodifferential evolution systems, Journal of Nonlinear Sciences and Applications, 4 (2011), no. 4, 281--291
AMA Style
Radhakrishnan B., Balachandran K., Controllability of nonlocal impulsive functional integrodifferential evolution systems. J. Nonlinear Sci. Appl. (2011); 4(4):281--291
Chicago/Turabian Style
Radhakrishnan , B., Balachandran, K.. "Controllability of nonlocal impulsive functional integrodifferential evolution systems." Journal of Nonlinear Sciences and Applications, 4, no. 4 (2011): 281--291
Keywords
- Controllability
- impulsive integrodifferential system
- evolution operator
- fixed point theorem
- nonlocal condition.
MSC
References
-
[1]
K. Balachandran, J. P. Dauer, Controllability of nonlinear systems via Fixed Point Theorems, J. Optim. Theory and Appl., 53 (1987), 345-352.
-
[2]
K. Balachandran, J. P. Dauer, Controllability of nonlinear systems in Banach spaces, A survey, J. Optim. Theory and Appl., 115 (2002), 7-28.
-
[3]
K. Balachandran, J. Y. Park, Existence of a mild solution of a functional integrodifferential equation with nonlocal condition, Bull.Korean Math. Soc., 38 (2001), 175-182.
-
[4]
K. Balachandran, M. Chandrasekaran, Existence of solutions of a delay differential equation with nonlocal condition, Indian. J. Pure Appl. Math., 27 (1996), 443-449.
-
[5]
L. Byszewski, V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a banach space, Appl. Anal. , 40 (1991), 11-19.
-
[6]
L. Byszewski , Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl., 162 (1991), 494-505.
-
[7]
L. Byszewski, H. Akca, On a mild solutions of a semilinear functional differential evolution nonlocal problem, J. Appl. Math. Stoch. Anal., 3 (1997), 265-271.
-
[8]
L. Byszewski, H. Akca, Existence of solutions of a semilinear functional-differential evolution nonlocal problem, Nonlinear Anal., 34 (1998), 65-72.
-
[9]
Y. K. Chang, Controllability of impulsive functional differential systems with infinite delay in Banach spaces, Chaos, Solitons and Fractals , 33 (2007), 1601-1609.
-
[10]
A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York (1969)
-
[11]
X. Fu, Y. Cao , Existence for neutral impulsive differential inclusions with nonlocal conditions, Nonlinear Anal., 68 (2008), 3707-3718.
-
[12]
D. Guo, X. Liu, Extremal solutions of nonlinear impulsive integrodifferential equations in Banach spaces, J. Math. Anal. Appl., 177 (1993), 538-552.
-
[13]
R. K. George, A. K. Nandakumaran, A. Arapostathis, A note on controllability of impulsive systems, J. Math. Anal. Appl., 241 (2000), 276-283.
-
[14]
Z. H. Guan, T. H. Qian, X. Yu , On controllability and observability for a class of impulsive systems, Systems and Control Letters, 47 (2002), 247-257.
-
[15]
V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore (1989)
-
[16]
M. Li, M. Wang, F. Zhang , Controllability of impulsive functional differential systems in Banach spaces, Chaos, Solitons and Fractals, 29 (2006), 175-181.
-
[17]
Y. Lin, J. H. Liu , Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear Anal., 26 (1996), 1023-1033.
-
[18]
J. Liang , J. H. Liu, T. J. Xiao, Nonlocal impulsive problems for nonlinear differential equations in Banach spaces, Math. Comp. Modelling, 49 (2009), 798-804.
-
[19]
A. Pazy , Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer- Verlag, New York (1983)
-
[20]
B. Radhakrishnan, K. Balachandran , Controllability of impulsive neutral functional evolution integrodifferential systems with infinite delay, Nonlinear Anal.: Hybrid Sys., 5 (2011), 655-670.
-
[21]
A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995)
-
[22]
G. Xie, L. Wang, Controllability and observability of a class of linear impulsive systems , J. Math. Anal. Appl., 304 (2005), 336-355.