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Controllability of semilinear systems with fixed delay in control

Kumar S., Sukavanam N.

Opuscula Mathematica

2015

Vol. 35, no. 1

71--83

In this paper, different sufficient conditions for exact controllability of semilinear systems with a single constant point delay in control are established in infinite dimensional space. The existence and uniqueness of mild solution is also proved under suitable assumptions. In particular, local Lipschitz continuity of a nonlinear function is used. To illustrate the developed theory some examples are given.

Controllability of mixed Volterra–Fredholm type integrodifferential third order dispersion equations

Kumar M., Sukavanam N.

Journal of Applied Analysis

2015

Vol. 21, nr 1

1--7

In this paper, we establish a result concerning the controllability of a mixed Volterra–Fredholm type integrodifferential third order dispersion equation. The result is obtained by using the theory of strongly continuous semigroups and the Banach fixed point theorem.