• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.131-145
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• 1991

The purpose of this paper is to prove the approximate controllability results, which were shown in [4] for the abstract semilinear control system, here, for the delay volterra system in the case of trajectories.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.173-181
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• 2012

In this paper, we study the control problems governed by the semilinear parabolic type equation in Hilbert spaces. Under the Lipschitz continuity condition of the nonlinear term, we can obtain the sufficient conditions for the approximate controllability of nonlinear functional equations with nonlinear monotone hemicontinuous and coercive operator. The existence, uniqueness and a variation of solutions of the system are also given.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.1-8
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• 2011

The approximate controllability for the nonlinear control system with nonlinear monotone hemicontinuous and coercive operator is studied. The existence, uniqueness and a variation of solutions of the system are also given.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.213-230
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• 2002

We deal with the approximate controllability for semilinear systems with time delay in a Hilbert space. First, we show the existence and uniqueness of solutions of the given systems with the mere general Lipschitz continuity of nonlinear operator f from $R\;\times\;V$ to H. Thereafter, it is shown that the equivalence between the reachable set of the semilinear system and that of its corresponding linear system. Finally, we make a practical application of the conditions to the system with only discrete delay.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.559-581
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• 2021

In this paper, we establish the existence of solutions and the approximate controllability for the semilinear neutral differential control system under natural assumptions such as the local Lipschitz continuity of nonlinear term. First, we deal with the regularity of solutions of the neutral control system using fractional powers of operators. We also consider the approximate controllability for the semilinear neutral control equation, with a control part in place of a forcing term, using conditions for the range of the controller without the inequality condition as in previous results.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.189-207
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• 2021

In this paper, we consider the approximate controllability for a class of semilinear integro-differential functional control equations in which nonlinear terms of given equations satisfy quasi-homogeneous properties. The main method used is to make use of the surjective theorems that is similar to Fredholm alternative in the nonlinear case under restrictive assumptions. The sufficient conditions for the approximate controllability is obtain which is different from previous results on the system operator, controller and nonlinear terms. Finally, a simple example to which our main result can be applied is given.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.881-891
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• 2012

In this paper we investigate the approximate controllability for the following nonlinear functional differential control problem: $$x^{\prime}(t)+Ax(t)+{\partial}{\phi}(x(t)){\ni}f(t,x(t))+h(t)$$ which is governed by the variational inequality problem with nonlinear terms.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.63-79
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• 2018

In this paper, we first consider the existence and regularity of solutions of the semilinear control system under natural assumptions such as the local Lipschtiz continuity of nonlinear term. Thereafter, we will also establish the approximate controllability for the equation when the corresponding linear system is approximately controllable.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.4
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• pp.355-368
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• 2021

In this paper, we investigate necessary and sufficient conditions for the approximate controllability for semilinear stochastic functional differential equations with delays in Hilbert spaces without the strict range condition on the controller even though the equations contain unbounded principal operators, delay terms and local Lipschitz continuity of the nonlinear term.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.623-631
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• 2005

The approximate controllability for the nonlinear control system with nonlinear monotone hemicontinuous and coercive operator is studied. The existence, uniqueness and a variation of solutions of the system are also given.