Existence results for a damped second order abstract functional differential equation with impulses

Controllability of Damped Second-Order Neutral Impulsive Stochastic Functional Differential Systems with Infinite Delay

“…Sakthivel [20] studied controllability of second order nonlinear impulsive differential systems. Hernandez et al [21] have explored the existence results for a damped second order abstract functional differential equation with impulses. Mahmudov and McKibben [22] discussed the abstract second order damped Mckean-Vlasov stochastic evolution equations.…”

Controllability of impulsive second-order nonlinear systems with nonlocal conditions in Banach spaces

“…The phenomenon of damped second-order equations can be found in Ball (1973), Fitzgibbon (1982), Balachandran and Park (2001), Hernandez, Balachandran, and Annapoorani (2009). The physical basis of the problem lies in the study of the dynamical buckling of a hinged extensible beam, which is either stretched or compressed by an axial force (Woinowsky-Krieger, 1950) and modelled by the hyperbolic equation…”

An Existence Result for Nonlocal Impulsive Second-Order Cauchy Problems with Finite Delay

“…On the other hand, the impulsive conditions have advantages over traditional initial value problems because they can be used to model phenomena that cannot be modeled by traditional initial value problems, such as the dynamics of populations subject to abrupt changes (harvesting, diseases, etc.) (see [16][17][18][19][20][21][22][23][24][25][26][27] and references therein). For this reason, the theory of impulsive differential equations has become an important area of investigation in recent years.…”

“…For this reason, the theory of impulsive differential equations has become an important area of investigation in recent years. Partial differential equations of first and second order with impulses have been studied by Rogovchenko [26], Liu [25], Cardinali and Rubbioni [19], Liang et al [24], Henríquez and Vásquez [1], Hernández et al, [21][22][23], Arthi and Balachandran [17], and so forth.…”