Controllability of neutral evolution integrodifferential systems with state dependent delay. (English) Zbl 1237.93029
Summary: In this paper, we address the problem of controllability of neutral evolution integrodifferential systems with state dependent delay in a Banach space. The results are obtained by using the theory of resolvent operators.
MSC:
| 93B05 | Controllability |
| 93C25 | Control/observation systems in abstract spaces |
| 47A05 | General (adjoints, conjugates, products, inverses, domains, ranges, etc.) |
Keywords:
controllability; integrodifferential system; evolution operator; resolvent operators; state dependent delayReferences:
| [1] | Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, New York (1983) · Zbl 0516.47023 |
| [2] | Adimy, M., Ezzinbi, K.: A class of linear partial neutral functional-differential with nondense domain. J. Differ. Equ. 147, 285–332 (1998) · Zbl 0915.35109 · doi:10.1006/jdeq.1998.3446 |
| [3] | Balachandran, K., Leelamani, A.: Controllability of neutral functional evolution integrodifferential systems with infinite delay. IMA J. Math. Control Inf. 25, 157–171 (2008) · Zbl 1146.93006 · doi:10.1093/imamci/dnm013 |
| [4] | Diagana, T., Hernandez, E., dos Santos, J.P.C.: Existence of asymptotically almost automorphic solutions to some abstract partial neutral integrodifferential equations. Nonlinear Anal., Theory Methods Appl. 71, 248–257 (2009) · Zbl 1172.45002 · doi:10.1016/j.na.2008.10.046 |
| [5] | Radhakrishnan, B., Balachandran, K.: Controllability results for second order neutral impulsive integrodifferential systems. J. Optim. Theory Appl. (2011). doi: 10.1007/s10957-011-9860-0 · Zbl 1234.93018 |
| [6] | Radhakrishnan, B., Balachandran, K.: Controllability of impulsive neutral functional evolution integrodifferential systems with infinite delay. Nonlinear Anal. Hybrid Syst. 5, 655–670 (2011) · Zbl 1227.93016 · doi:10.1016/j.nahs.2011.05.001 |
| [7] | Wang, L., Wang, Z.: Controllability of abstract neutral functional differential systems with infinite delay. Dyn. Contin. Discrete Impuls. Syst. 9, 59–70 (2002) · Zbl 1001.93005 |
| [8] | Fu, X.: Controllability of abstract neutral functional differential systems with unbounded delay. Appl. Math. Comput. 141, 299–314 (2004) · Zbl 1044.93008 · doi:10.1016/S0096-3003(03)00342-4 |
| [9] | Balachandran, K., Dauer, J.P.: Controllability of nonlinear systems via Fixed Point Theorems. J. Optim. Theory Appl. 53, 345–352 (1987) · Zbl 0596.93010 · doi:10.1007/BF00938943 |
| [10] | Bartha, M.: Periodic solutions for differential equations with state-dependent delay and positive feedback. Nonlinear Anal., Theory Methods Appl. 53, 839–857 (2003) · Zbl 1028.34062 · doi:10.1016/S0362-546X(03)00039-7 |
| [11] | Cao, Y., Fan, J., Gard, T.C.: The efforts of state-dependent time delay on a stage-structure population growth model. Nonlinear Anal., Theory Methods Appl. 19, 95–105 (1992) · Zbl 0777.92014 · doi:10.1016/0362-546X(92)90113-S |
| [12] | Hartung, F.: Linearized stability in periodic functional differential equations with state-dependent delays. J. Comput. Appl. Math. 174, 201–211 (2005) · Zbl 1077.34074 · doi:10.1016/j.cam.2004.04.006 |
| [13] | Hartung, F., Turi, J.: Identification of parameters in delay equations with state-dependent delays. Nonlinear Anal., Theory Methods Appl. 11, 1303–1318 (1997) · Zbl 0894.34071 · doi:10.1016/S0362-546X(96)00100-9 |
| [14] | Hernandez, E., Ladeira, L., Prokopczyk, A.: A note on state dependent partial functional differential equations with unbounded delay. Nonlinear Anal., Real World Appl. 7, 510–519 (2006) · Zbl 1109.34060 · doi:10.1016/j.nonrwa.2005.03.014 |
| [15] | Hernandez, E., McKibben, M.: On state-dependent delay partial neutral functional differential equations. Appl. Math. Comput. 186, 294–301 (2007) · Zbl 1119.35106 · doi:10.1016/j.amc.2006.07.103 |
| [16] | Hernandez, E., McKibben, M., Henriquez, H.: Existence results for partial neutral functional differential equations with state-dependent delay. Math. Comput. Model. 49, 1260–1267 (2009) · Zbl 1165.34420 · doi:10.1016/j.mcm.2008.07.011 |
| [17] | Hernandez, E., Pierri, M., Goncalves, G.: Existence results for an impulsive abstract partial differential equation with state-dependent delay. Comput. Math. Appl. 52, 411–420 (2006) · Zbl 1153.35396 · doi:10.1016/j.camwa.2006.03.022 |
| [18] | Da Parto, G., Iannelli, M.: Existence and regularity for a class of integrodifferential equations of parabolic type. J. Math. Anal. Appl. 112, 36–55 (1985) · Zbl 0583.45009 · doi:10.1016/0022-247X(85)90275-6 |
| [19] | Grimmer, R.C., Pritchard, A.: Analytic resolvent operators for integral equations in Banach space. J. Differ. Equ. 50, 234–259 (1983) · Zbl 0519.45011 · doi:10.1016/0022-0396(83)90076-1 |
| [20] | Balachandran, K., Dauer, J.P.: Controllability of nonlinear systems in Banach spaces: a survey. J. Optim. Theory Appl. 115, 7–28 (2002) · Zbl 1023.93010 · doi:10.1023/A:1019668728098 |
| [21] | Chukwu, E.N., Lenhart, S.M.: Controllability questions for nonlinear systems in abstract spaces. J. Optim. Theory Appl. 68, 437–462 (1991) · Zbl 0697.49040 · doi:10.1007/BF00940064 |
| [22] | Radhakrishnan, B., Balachandran, K.: Controllability results for semilinear impulsive integrodifferential evolution systems with nonlocal conditions. J. Control Theory Appl. (to appear) · Zbl 1265.93023 |
| [23] | Yan, Z.: Controllability of semilinear integrodifferential systems with nonlocal conditions. Int. J. Comput. Appl. Math. 3, 221–236 (2007) |
| [24] | Zhang, X.: Exact controllability of semilinear evolution systems and its application. J. Optim. Theory Appl. 107, 415–432 (2000) · Zbl 0966.47044 · doi:10.1023/A:1026460831701 |
| [25] | dos Santos, J.P.C.: On state-dependent delay partial neutral functional integrodifferential equations. Appl. Math. Comput. 216, 1637–1644 (2010) · Zbl 1196.45013 · doi:10.1016/j.amc.2010.03.019 |
| [26] | dos Santos, J.P.C.: Existence results for a partial neutral integrodifferential equation with state-dependent delay. Elect. J. Qualitative Theory Differ. Equ. 29, 1–12 (2010) · Zbl 1208.45009 |
| [27] | dos Santos, J.P.C., Henriquez, H., Hernandez, E.: Existence results for neutral integrodifferential equations with unbounded delay. J. Integral Equ. Appl. 23, 289–330 (2011) · Zbl 1228.45019 · doi:10.1216/JIE-2011-23-2-289 |
| [28] | Sadaovskii, B.: On a fixed point principle. Funct. Anal. Appl. 2, 151–153 (1967) |
| [29] | Hino, Y., Murakami, S., Naito, T.: Functional-Differential Equations with Infinite Delay. Lecture Notes in Mathematics, vol. 1473. Springer, Berlin (1991) · Zbl 0732.34051 |
| [30] | Martin, R.H.: Nonlinear Operators and Differential Equations in Banach Spaces. Krieger, Melbourne (1987) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
