Controllability for systems governed by semilinear differential inclusions in a Banach space with a noncompact semigroup

The monotone method for controllability of the nonlinear evolution systems

“…However, the controllability results are only true for the ordinary differential systems in finite-dimensional spaces if the corresponding operator semigroup is compact [1] , and it is known that in infinite-dimensional case the associated linear system is not controllable (see [4,15,22]). Very recently Balachandran and Obukhovski et al [2,16] studied the controllability of evolution systems without compactness conditions. In [2], the author's idea is to fix a desirable state and then to determine a control u so that the corresponding solution is approximately or exactly equal to the desirable state.…”

“…In [2], the author's idea is to fix a desirable state and then to determine a control u so that the corresponding solution is approximately or exactly equal to the desirable state. In [16], the authors use the Hausdorff measure of noncompactness to obtain the result.…”

Semilinear Nonlocal Differential Equations With Delay Terms

“…In recent years, Obukhovski and Zecca [6] discussed the controllability for the system governed by semilinear differential inclusions in a Banach space with noncompact semigroup and Xue [7,8] studied semilinear nonlocal problems without the assumption of compactness in Banach spaces. Zhu et el.…”

Controllability results for impulsive differential systems with finite delay

“…The concept of controllability plays an important role in many areas of applied mathematics. In recent years, significant progress has been made in the controllability of linear and nonlinear deterministic systems [6,11,17,19]. In [11], the author studied the controllability of impulsive functional differential systems of the form x (t) = A(t)x(t) + f (t, x(t)) + (Bu)(t), a.e.…”