Exact null controllability for semilinear differential equations with nonlocal conditions in Hilbert spaces

Abstract

We present some sufficient conditions for the exact null controllability of semilinear differential equations with nonlocal conditions in Hilbert spaces. By using operator semigroups and fixed point theorems, we obtain some new results on exact null controllability when the nonlocal item is Lipschitz continuous and is neither Lipschitz nor compact, respectively. The method in this paper can also be applied to other nonlocal differential systems to weaken the compactness of nonlocal item. An example concerning the partial differential equation is presented to illustrate our results.