Approximate controllability of non-densely defined semilinear control systems for two classes of nonlinearity

In this article, some sufficient conditions are given for approximate controllability of the semilinear control systems in which the state linear operator is defined on an infinite dimensional Banach space with non-dense domain. This article has two main sections. In the first section, the approximate controllability is proved with nonlinearity satisfying the monotone condition and in the second section with nonlinearity satisfying integral contractor condition.