Mild solution and controllability of second-order non-local retarded semilinear systems

Existence and controllability of second‐order nonlinear retarded integro‐differential systems with multiple delays in control

“…Remark Kumar and Tomar [6] studied the exact controllability of nonlinear retarded systems of second‐order. In their work [7], Haq and Sukavanam extended the result of Kumar and Tomar [6], and they investigated the controllability of retarded systems with constant delay in control.…”

“…Remark Kumar and Tomar [6] studied the exact controllability of nonlinear retarded systems of second‐order. In their work [7], Haq and Sukavanam extended the result of Kumar and Tomar [6], and they investigated the controllability of retarded systems with constant delay in control. In the present paper, we relax the conditions [ H 3 ], [ H 4 ], and [ H 5 ] of Haq and Sukavanam [7] and prove the controllability of nonlinear retarded integro‐differential systems of second order involving several constant delays in control by applying different approach.…”

“…The stochastic controllability of impulsive differential equations involving constant delays in state was proved in [8]. Recently, controllability results for second‐order retarded systems were proved in [6, 7]. However, the controllability of second‐order nonlinear retarded integro‐differential systems involving constant delays is still an untreated topic, and this fact is the motivation of the present work.…”

“…The controllability concept has become an active area of research due to its huge applications in the field of physics. There are many articles on controllability of systems represented by differential inclusions and differential equations (see [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and references therein). Among them, controllability property for linear differential systems involving variable delay was discussed in [5].…”