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We consider a nonlinear degenerate reaction-diffusion equation. First we prove that if the initial state is nonnegative, then the solution remains nonnegative for all time. Then we prove the approximate controllability between nonnegative states via multiplicative controls, this is done using the reaction coefficient as control.

In this article, we study the approximate controllability for quasilinear differential equations with deviating arguments in a Hilbert space. We establish sufficient conditions for the existence of a mild solution. We also obtain sufficient conditions for the controllability of quasilinear equations. Further, we use it to establish the approximate controllability for quasilinear differential equations with deviating arguments. We discuss examples in which the analytical results are applied.

In this article, we study an Euler-Bernoulli viscoelastic control system which is dissipative due to the presence of the viscoelastic term. The main feature which distinguishes this paper from other related works lies in the fact that we no longer impose traditional conditions such as complete monotonicity and decay property on the kernel function g. Without loss of generality, we study the system in the case of $g\equiv 1$. By means of the duality principle and the Hahn-Banach theorem, we show that the system with g=1 is approximately controllable in the appropriate function space.

We consider a nonlinear degenerate reaction-discusion equation. First we prove that if the initial state is nonnegative, then the solution remains nonnegative for all time. Then we prove the approximate controllability between nonnegative states via multiplicative controls, this is done using the reaction coeficient as control. [ABSTRACT FROM AUTHOR]

The aim of this article is to establish sufficient conditions for the approximate controllability of fractional control systems with time delay in Hilbert spaces. By the technique of sequential approach, we prove that the fractional control systems with time delay are approximately controllable. Finally, an example is provided to illustrate our main results.

In this article, we study the approximate controllability and homegenization results of a semi-linear elliptic problem with Robin boundary condition in a periodically perforated domain. We prove the existence of minimal norm control using Lions constructive approach, which is based on Fenchel-Rockafeller duality theory, and by means of Zuazua's fixed point arguments. Then, as the homogenization parameter goes to zero, we link the limit of the optimal controls (the limit of fixed point of the controllability problems) with the optimal control of the corresponding homogenized problem.

The objective of this article is to prove sufficient conditions for the approximate controllability for a class of nonautonomous nonlocal finite delay differential equations with deviating arguments in a Hilbert space. We also establish sufficient conditions for the existence of mild solutions. The results are established using the fixed point theorem of Krasnoselskii and theory of semigroup of bounded linear operators. We discuss an example for the application of the analytical results.

In this article, we study the approximate controllability for quasilinear differential equations with deviating arguments in a Hilbert space. We establish sufficient conditions for the existence of a mild solution. We also obtain sufficient conditions for the controllability of quasilinear equations. Further, we use it to establish the approximate controllability for quasilinear differential equations with deviating arguments. We discuss examples in which the analytical results are applied. [ABSTRACT FROM AUTHOR]

This paper studies the approximate controllability of neutral stochastic integro-differential systems with impulsive effects. Sufficient conditions are formulated and proved for the approximate controllability. The results are obtained by using the Nussbaum fixed point theorem and the theory of analytic resolvent operator. An example is given to show the applications of the proposed results.

We study the controllability for a class of semilinear control problems in Hilbert spaces, for which the uniqueness is unavailable. Using the fixed point theory for multivalued maps with nonconvex values, we show that the nonlinear problem is approximately controllable provided that the corresponding linear problem is. We also obtain some results on the continuity of solution map and the topological structure of the solution set of the mentioned problem.

In this article, we study the approximate controllability and homegenization results of a semi-linear elliptic problem with Robin boundary condition in a periodically perforated domain. We prove the existence of minimal norm control using Lions constructive approach, which is based on Fenchel-Rockafeller duality theory, and by means of Zuazua's fixed point arguments. Then, as the homogenization parameter goes to zero, we link the limit of the optimal controls (the limit of fixed point of the controllability problems) with the optimal control of the corresponding homogenized problem. [ABSTRACT FROM AUTHOR]

The objective of this article is to prove sufficient conditions for the approximate controllability for a class of nonautonomous nonlocal finite delay differential equations with deviating arguments in a Hilbert space. We also establish suficient conditions for the existence of mild solutions. The results are established using the fixed point theorem of Krasnoselskii and theory of semigroup of bounded linear operators. We discuss an example for the application of the analytical results. [ABSTRACT FROM AUTHOR]

In this article, we study the approximate controllability of impulsive abstract fractional neutral evolution equations in Banach spaces. The main results are obtained by using Krasnoselkii's fixed point theorem, fractional calculus and methods of controllability theory. An application is provided to illustrate the theory. Here we have provided new definition of phase space for the impulsive and infinite delay term. Our result is new for the approximate controllability with infinite delay in Hilbert space.

In this paper sufficient conditions are established for the controllability of a class of neutral stochastic integrodifferential equations with nonlocal conditions in abstract space. The Nussbaum fixed point theorem is used to obtain the controllability results, which extends the linear system to the stochastic settings with the help of compact semigroup. An example is provided to illustrate the theory.

Approximate controllability problem for a linear distributed control system with possibly unbounded input operator, connected in a series to another distributed system without control is investigated. An initial state of the second distributed system is considered as a control parameter. Applications to control partial equations governed by hyperbolic controller, and to control delay systems governed by hereditary controller are considered.

In this paper we prove an approximate controllability result for an abstract semilinear evolution equation in a Hilbert space and we obtain as consequences the approximate controllability for some classes of elliptic and parabolic problems subjected to nonlinear, possible non monotone, dynamic boundary conditions.

In this paper sufficient conditions are established for the controllability of a class of neutral stochastic integrodifferential equations with nonlocal conditions in abstract space. The Nussbaum fixed point theorem is used to obtain the controllability results, which extends the linear system to the stochastic settings with the help of compact semigroup. An example is provided to illustrate the theory. [ABSTRACT FROM AUTHOR]