Controllability of nonlinear integro-differential third order dispersion system

In this short article, sufficient condition for controllability of nonlinear dispersion system is studied. The result is obtained by using the Schaefer fixed-point theorem. This work extends the work of Chalishajar, George and Nandakumaran [D.N. Chalishajar, R.K. George, A.K. Nandakumaran, Exact controllability of the third order nonlinear dispersion equation, J. Math. Anal. Appl. 332 (2007) 1028-1044]. Usually authors assume the compactness of semigroup while studying the controllability. Here we drop this assumption and prove the controllability result.