Controllability of Non-densely Defined Neutral Functional Differential Systems in Abstract Space*

Abstract

In this paper, by means of Sadovskii fixed point theorem, the authors establish a result concerning the controllability for a class of abstract neutral functional differential systems where the linear part is non-densely defined and satisfies the Hille-Yosida condition. As an application, an example is provided to illustrate the obtained result.

Keywords

Controllability / Non-densely defined / Integral solution / Sadovskii fixed point theorem / 34K30

References

[1] Chuckwu J. Optim. theory Appl., 1991, 68: 437

[2] Naito SIAM J. Control Optim., 1987, 25: 715

[3] Naito J. Optim. theory Appl., 1989, 61: 271

[4] Nakagri Internat. J. control, 1989, 49: 1489

[5] Triggiani SIAM J. Control Optim., 1975, 13: 462

[6] Lasiecka Appl. Math. Optim., 1991, 23: 109

[7] Quinn Numer. Funct. Anal. Optim., 1984/1985, 7: 197

[8] Kwun Bull. Korean Math. Soc., 1991, 28: 131

[9] Balachandran Appl. Math. Letters, 1999, 12: 63

[10] Balachandran J. Optim. Theory Appl., 1996, 88: 61

[11] Fu Appl. Math. Comp., 2003, 141: 281

[12] Da Prato Ann. Scuola Norm. Sup. Pisa Sci., 1987, 14: 285

[13] Gatsori J. Math. Anal. Appl., 2004, 297: 194

[14] Kellermann J. Funct. Anal., 1989, 84: 160

[15] Thiems J. Math. Anal. Appl, 1990, 152: 416

[16] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer- Verlag, New York, 1983