Existence for neutral impulsive differential inclusions with nonlocal conditions

Existence results for non-densely defined neutral impulsive differential inclusions with nonlocal conditions

“…In recent years existence problems for different kinds of dynamical systems have been considered in many publications [5,[9][10][11][12]. Akca et al [1], initiated the study of impulsive differential equations with nonlocal conditions in Banach spaces.…”

Generalized Cauchy problems involving nonlocal and impulsive conditions

“…See, for example, the papers [1,3,8,17,18,20], which are close to our problem in this work. Most studies in nonlocal or impulsive problems have been carried out with the feature that the nonlocal function or impulsive function is of Lipschitz type or is completely continuous, which allows to apply the Banach contraction principle or the Schauder fixed point theorem in order to get the solutions.…”

“…Most studies in nonlocal or impulsive problems have been carried out with the feature that the nonlocal function or impulsive function is of Lipschitz type or is completely continuous, which allows to apply the Banach contraction principle or the Schauder fixed point theorem in order to get the solutions. The mentioned nonlocal functions can be found in [3,8,19,25,29,30], while the impulsive functions imposed by Lipschitz or compactness assumptions are included in [1,17,20,23,33]. As another feature, when A is densely defined (D(A) = X ), the assumption that the semigroup generated by A is compact has been used in a numerous research.…”

“…This allows to reduce the Lipschitz or compactness assumptions on nonlocal, impulsive functions and on nonlinearity. See [17,18,20,23,29,32] for these cases. The case when A is nondensely defined has been considered by many authors recently.…”

Existence Results for a Second Order Impulsive Neutral Functional Integrodierential Inclusions in Banach Spaces with Innite Delay

“…For more details on impulsive theory and integrodifferential equations we refer to the monographs of Bainov and Simeonov [3], Lakshmikantham, Bainov, and Simeonov [43], Samoilenko and Perestyuk [51], Benchohra, Henderson and Ntouyas [7] and the papers of Rogovchenko [54], Liu [47], Hernandez [28,29,30,31,32,33], Anguraj et al [2], Balachandran et al [4,5,50], Benchohra et al [8,9,10], Ntouyas [49], Chang et al [15,16,17,18,19], Liang et al [45]. However, very few results are available for impulsive differential and integrodifferential inclusions; see for instance, the papers of Benchohra et al [11,12,13,14], Erbe and Krawcewicz [22], and Frigon et al [23], Xianlong Fu et al [24], Anguraj et al [20] and Junhao Hu et al [39].…”