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Controllability of Volterra-Fredholm type systems in Banach spaces. (English) Zbl 1160.93005
Summary: We show the results in D. N. Chalishajar [J. Franklin Inst. 344, No. 1, 12–21 (2007; Zbl 1119.93016)] and Y.-K. Chang and D. N. Chalishajar [Controllability of mixed Volterra-Fredholm type integro-differential systems in Banach spaces, J. Franklin Inst. 345, 499–507 (2008), doi:10.1016/j.jfranklin.2008.02.002] are only valid for ordinary differential control systems. As a result the examples provided cannot be recovered as applications of the abstract results.
MSC:
93B05Controllability
93C23Systems governed by functional-differential equations
93C25Control systems in abstract spaces
45J05Integro-ordinary differential equations
References:
[1]Chalishajar, D. N.: Controllability of mixed Volterra – Fredholm-type integro-differential systems in Banach space, J. franklin inst. 344, No. 1, 12-21 (2007) · Zbl 1119.93016 · doi:10.1016/j.jfranklin.2006.04.002
[2]Chang, Y. -K.; Chalishajar, D. N.: Controllability of mixed Volterra – Fredholm type integro-differential systems in Banach space, J. franklin inst. 345, No. 5, 499-507 (2008) · Zbl 1167.93007 · doi:10.1016/j.jfranklin.2008.02.002
[3]Grimmer, R. C.: Resolvent operators for integral equations in a Banach space, Trans. am. Math. soc. 273, No. 1, 333-349 (1982) · Zbl 0493.45015 · doi:10.2307/1999209
[4]Henríquez, H. R.: On nonexact controllable systems, Int. J. Control 42, No. 1, 71-83 (1985) · Zbl 0569.93008 · doi:10.1080/00207178508933347
[5]Triggiani, R.: A note on the lack of exact controllability for mild solutions in Banach spaces, SIAM J. Control optim. 15, No. 3, 407-411 (1977) · Zbl 0354.93014 · doi:10.1137/0315028
[6]Triggiani, R.: Addendum: ”A note on the lack of exact controllability for mild solutions in Banach spaces” [ SIAM J. Control optim. 15(3)(1977) 407 – 411; MR 55 8942], SIAM J. Control optim. 18, No. 1, 98-99 (1980)
[7]Chang, Y. -K.; Li, W. -T.; Nieto, J. J.: Controllability of evolution differential inclusions in Banach spaces, Nonlinear anal. 67, No. 2, 623-632 (2007) · Zbl 1128.93005 · doi:10.1016/j.na.2006.06.018
[8]Liu, B.: Controllability of nonlinear neutral evolution integrodifferential systems with infinite delay, J. optim. Theory appl. 122, No. 1, 87-109 (2004) · Zbl 1130.93313 · doi:10.1023/B:JOTA.0000041732.08947.0c
[9]Balasubramaniam, P.; Ntouyas, S. K.: Controllability for neutral stochastic functional differential inclusions with infinite delay in abstract space, J. math. Anal. appl. 324, No. 1, 161-176 (2006) · Zbl 1118.93007 · doi:10.1016/j.jmaa.2005.12.005