Approximate controllability of semilinear partial functional differential systems

P. Balasubramaniam and S. K. Ntouyas, Controllability for neutral stochastic functional differential inclusions with infinite delay in abstract space. J. Math. Anal. Appl. 324 (2006), 161–176.

A. E. Bashirov and N. I. Mahmudov, On concepts of controllability for linear deterministic and stochastic systems. SIAM J. Control Optim. 37 (1999), 1808–1821.

A. Bensoussan, G. Da Prato, M. C. Delfour, and S. K. Mitter, Representation and control of infinite-dimensional systems. Vol. 2. Systems and control: Foundations and applications. Birkhäuser, Boston (1993).

E. N. Chuckwu and S. M. Lenhart, Controllability questions for nonlinear systems in abstract spaces. J. Optim. Theory Appl. 68 (1991), 437–462.

R. Curtain and H. J. Zwart, An introduction to infinite-dimensional linear systems theory. Springer-Verlag, New York (1995).

J. P. Dauer and N. I. Mahmudov, Approximate controllability of semilinear functional equations in Hilbert spaces. J. Math. Anal. Appl. 273 (2002), 310–327.

V. N. Do, A note on approximate controllability of semilinear systems. Systems control Lett. 12 (1989), 365–371.

X. Fu and X. Liu, Existence of periodic solutions for abstract neutral non-autonomous equations with infinite delay. J. Math. Anal. Appl. 325 (2007), 249–267.

R. J. George, Approximate controllability of nonautonomous semilinear systems. Nonlin. Anal. 24 (1995), 1377–1393.

J. Hale and S. M. Verduyn Lunel, Introduction to functional differential equations. Springer-Verlag, New York (1993).

E. Hernández and H. R. Henríquez, Existence results for partial neutral functional differential equations with unbounded delay. J. Math. Anal. Appl. 221 (1998), 452–475.

M. C. Joshi and N. Sukavanam, Approximate solvability of semilinear operator equations. Nonlinearity 3 (1990), 519–525.

J. Klamka, Constrained controllability of nonlinear systems J. Math. Anal. Appl. 201 (1996), 365–674.

X. Li and J. Yong, Optimal control theory for infinite-dimensional systems. Birkhäuser, Berlin (1995).

K. Naito, Controllability of semilinear control systems dominated by the linear part. SIAM J. Control Optim. 25 (1987), 715–722.

_____, Approximate controllability for trajectories of semilinear control systems J. Optim. Theory Appl. 60 (1989), 57–65.

N. S. Papageorgiou, Controllability of infinite-dimensional systems with control constraints. J. Math. Anal. Appl. 186 (1994), 523–533.

A. Pazy, Semigroups of linear operators and applications to partial differential equations. Springer-Verlag, New York (1983).

B. N. Sadovskii, On a fixed point principle. Funct. Anal. Appl. 1 (1967), 74–76.

R. Sakthivel, N. I. Mahmudov, and J. H. Kim, Approximate controllability of nonlinear impulsive differential systems. Repts. Math. Phys. 60 (2007), 85–96.

A. M. Samoilenko and N. A. Perestyuk, Impulsive differential equations. World Scientific, Singapore (1995).

C. C. Travis and G. F. Webb, Existence, stability, and compactness in the α-norm for partial functional differential equations. Trans. Amer. Math. Soc. 240 (1978), 129–143.

J. Wu, Theory and applications of partial functional differential equations. Springer-Verlag (1996).

M. Yamamoto and J. Y. Park, Controllability for parabolic equations with uniformly bounded nonlinear terms. J. Optim. Theory Appl. 66 (1990), 515–532.

T. Yang, Impulsive systems and control: Theory and applications. Springer-Verlag, Berlin (2001).

J. Zabczyk, Mathematical control theory. Birkhäuser, Berlin (1992).

H. X. Zhou, Approximate controllability for a class of semilinear abstract equations. SIAM J. Control Optim. 21 (1983), 551–565.