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In this investigation. our primary concentration is placed on an impulsive resolvent integro-differential inclusions (IRIDI) in Hilbert spaces. The topic of discussion for this investigation is the approximation of controllability (AC) for an IRIDI in Hilbert spaces. We provide a set 01 necessary criteria for the AC of nonlinear IRIDI in Hilbert spaces by making use of Bolinenblust-Karlin's (B-K) fixed point theorem. These constraints pertain to the fact that the inclusions must be nonlinear. [ABSTRACT FROM AUTHOR]

We consider here a semilinear heat equation with the source term as well as the initial and boundary conditions are partially known. We are interesting in a sentinel [6] problem, which consists in finding the pollution term without any attempt of computing the perturbation. We present here some case of approached sentinels. We prove the existence of such sentinel by solving a problem of approximate controllability. To deal with the approximate controllability problem, we make use of the theory of duality in convex optimization following Fenchel-Rockafellar. [ABSTRACT FROM AUTHOR]

In this paper, the existence results for approximate controllability of random impulsive semilinear neutral functional differential system with less restrictive conditions are studied. The domain of the linear operator is not dense in the space defined. Finally, examples are given to illustrate the applications of our results. [ABSTRACT FROM AUTHOR]

This paper concerns with the approximate controllability of second-order impulsive stochastic differential equations with nonlocal conditions in Hilbert space setting. Using stochastic analysis and fixed point scheme, a new set of sufficient conditions is formulated that ensures the approximate controllability of the considered system. Finally, an example is included to illustrate effectiveness of the developed theory. [ABSTRACT FROM AUTHOR]

On the account of semigroup theory, fractional calculus, the strategy of fractional powers of operators, α-norm and Krasnoselskii's fixed point theorem, this manuscript explores some necessary conditions to establish the approximate controllability results of fractional integro- differential systems with nonlocal and finite delay conditions regarded in a Hilbert space. [ABSTRACT FROM AUTHOR]

In this paper, by using the theory of strongly continuous cosine family and Schauder's fixed point theorem, we study the approximate controllability of second order semilinear delay control systems. As application, an example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of approximate controllability of random impulsive semilinear control system under a sufficient condition with non-densely defined system. Finally, eximples are given to illustrate the applications of the abstract results. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present some sufficient conditions for approximate controllability of fractional order semilinear system of order α ∊ (1,2] in Hilbert spaces. The results are obtained by using Schauder's fixed point theorem. At the end, an example is given to show the effectiveness of the result. [ABSTRACT FROM AUTHOR]

The approximate controllability of a fractional impulsive stochastic neutral integro-differential equation with deviating argument and infinite delay is studied. The control parameter being inside the nonlinear term. Only Schauder fixed point theorem and a few fundamental hypotheses are used to prove our result. The assumption of the existence of the inverse of controllability operator is not required. Since its inverse does not exist in infinite dimensional space if the associated semigroup is compact. Lipschitz continuity of the nonlinear function is also not required. We also give an example to illustrate our result. [ABSTRACT FROM AUTHOR]

In this paper, using the Schauder's fixed point theorem, different sufficient conditions to the approximate controllability for a class of retarded semilinear control systems with bounded delay are established. The paper is also concerned with the existence and uniqueness of mild solution. In particular, to obtain desired results it is assumed that the nonlinear function is locally Lipschitz continuous and satisfies linear growth condition. This theory relax the assumptions on nonlinear term of the semilinear system made by earlier authors. Finally, an example is given to show the application of the main result. [ABSTRACT FROM AUTHOR]

In this article, we establish the sufficient conditions for the approximate controllability for a class of fractional neutral integro-differential inclusions with state-dependent delay in Hilbert spaces. The results are obtained by using the fixed point theorem for discontinuous multi-valued operators due to Dhage with the resolvent operator. An example is provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, we prove the approximate controllability for a class of semilinear delay control systems of fractional order under the natural assumption that the corresponding linear system is approximately controllable. The theory is illustrated with an example. [ABSTRACT FROM AUTHOR]