Controllability results for nondensely defined semilinear functional differential equations. (English) Zbl 1101.93007
Summary: We investigate the controllability of first-order semilinear functional and neutral functional differential equations in Banach spaces.
MSC:
| 93B05 | Controllability |
| 93C23 | Control/observation systems governed by functional-differential equations |
Keywords:
controllability; functional semilinear differential equations; nondensely defined operator; fixed point; semigroup; measurable; Banach spaceReferences:
| [1] | Arendt, W., Vector valued Laplace transforms and Cauchy problems. Israel J. Math. 59 (1987), 327 - 352. · Zbl 0637.44001 · doi:10.1007/BF02774144 |
| [2] | Balachandran, K. and Balasubramaniam, P., Remarks on the controllability of nonlinear perturbations of Volterra integrodifferential systems. J. Appl. Math. Stochastic Anal. 8 (1995), 201 - 208. · Zbl 0826.93007 · doi:10.1155/S1048953395000190 |
| [3] | Balachandran, K. Balasubramaniam, P. and Dauer, J. P., Controllability of nonlinear integrodifferential systems in Banach space. J. Optim. Theory Appl. 84 (1995), 83 - 91. · Zbl 0821.93010 · doi:10.1007/BF02191736 |
| [4] | Balachandran, K., Balasubramaniam, P. and Dauer, J. P., Local null control- lability of nonlinear functional-differential systems in Banach space. J. Optim. Theory Appl. 88 (1996), 61 - 75. · Zbl 0848.93007 · doi:10.1007/BF02192022 |
| [5] | Balachandran, K. and Dauer, J. P., Controllability of nonlinear systems in Banach spaces: a survey. Dedicated to Professor Wolfram Stadler. J. Optim. Theory Appl. 115 (2002), 7 - 28. · Zbl 1023.93010 · doi:10.1023/A:1019668728098 |
| [6] | Balachandran, K., Dauer, J. P. and Sangeetha, S., Controllability of nonlinear evolution delay integrodifferential systems. Appl. Math. Comput. 139 (2003), 63 - 84. · Zbl 1024.93004 · doi:10.1016/S0096-3003(02)00169-8 |
| [7] | Balachandran, K. and Manimegalai, P., Controllability of nonlinear abstract neutral evolution integrodifferential systems. Nonlinear Funct. Anal. Appl. 7 (2002), 85 - 100. · Zbl 0997.93012 |
| [8] | Balachandran, K. and Sakthivel, R., A note on controllability of semilinear integrodifferential systems in Banach spaces. J. Appl. Math. Stochastic Anal. 13 (2000), 161 - 170. 325 · Zbl 0964.93010 · doi:10.1155/S1048953300000174 |
| [9] | Benchohra, M., Gatsori, E., Henderson, J. and Ntouyas, S. K., Nondensely defined evolution impulsive differential inclusions with nonlocal conditions. J. Math. Anal. Appl. 286 (2003), 307 - 325. · Zbl 1039.34056 · doi:10.1016/S0022-247X(03)00490-6 |
| [10] | Benchohra, M., Gatsori, E., Górniewicz, L. and Ntouyas, S. K., Nondensely de- fined evolution impulsive differential equations with nonlocal conditions. Fixed Point Theory 4 (2003), 185 - 204. · Zbl 1060.34027 |
| [11] | Benchohra, M., Górniewicz, L., Ntouyas, S. K. and Ouahab, A., Existence re- sults for nondensely defined impulsive semilinear functional differential equa- tions. In: Nonlinear Analysis and Applications: to V. Lakshmikantham on his 80th birthday (eds: Ravi P. Agarwal and Donal O’Regan), Vol. 1, 2. Dordrecht: Kluwer Acad. Publ. 2003, pp. 289 - 300. · Zbl 1051.34068 |
| [12] | Byszewski, L., Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. J. Math. Anal. Appl. 162 (1991), 494 - 505. · Zbl 0748.34040 · doi:10.1016/0022-247X(91)90164-U |
| [13] | Da Prato, G. and Sinestrari, E., Differential operators with non-dense domains. Ann. Scuola Norm. Sup. Pisa Sci. 14 (1987), 285 - 344. · Zbl 0652.34069 |
| [14] | Dauer, J. P. and Mahmudov, N., Approximate controllability of semilin- ear functional equations in Hilbert spaces. J. Math. Anal. Appl. 273 (2002), 310 - 327. · Zbl 1017.93019 · doi:10.1016/S0022-247X(02)00225-1 |
| [15] | Dugundji, J. and Granas, A., Fixed Point Theory. Warsaw: Mongrafie Mat. PWN 1982. · Zbl 0483.47038 |
| [16] | Ezzinbi, K. and Liu, J., Nondensely defined evolution equations with nonlocal conditions. Math. Comput. Modelling 36 (2002), 1027 - 1038. · Zbl 1035.34063 · doi:10.1016/S0895-7177(02)00256-X |
| [17] | Gatsori, E., Controllability results for nondensely defined evolution differ- ential inclusions with nonlocal conditions. J. Math. Anal. Appl. 297 (2004), 194 - 211. · Zbl 1059.34037 · doi:10.1016/j.jmaa.2004.04.055 |
| [18] | Kellermann, H. and Hieber, M., Integrated semigroup. J. Funct. Anal. 84, (1989), 160 - 180. · Zbl 0689.47014 · doi:10.1016/0022-1236(89)90116-X |
| [19] | Lakshmikantham, V., Bainov, D. D. and Simeonov, P. S., Theory of Impulsive Differential Equations. Singapore: World Scientific 1989. · Zbl 0719.34002 |
| [20] | Lakshmikantham, V. and Leela, S., Differential and Integral Inequalities, Vol. I. New York: Academic Press 1969. · Zbl 0177.12403 |
| [21] | McKibben, M., A note on the approximate controllability of a class of abstract semi-linear evolution equations. Far. East J. Math. Sci. (FJMS) 5 (2002), 113 - 133. · Zbl 1005.93008 |
| [22] | Smart, D. R.: Fixed Point Theorems. Cambridge: Cambridge Univ. Press 1974. · Zbl 0297.47042 |
| [23] | Yosida, K.: Functional Analysis (6th edn.). Berlin: Springer 1980. · Zbl 0435.46002 |
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.
