• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.757-769
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• 2008

This paper deals with the existence of optimal controls and maximal principles for semilinear evolution equations with the nonlinear term satisfying Lipschitz continuity. We also present the necessary conditions of optimality which are described by the adjoint state corresponding to the linear equations without a condition of differentiability for nonlinear term.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.04a
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• pp.213-216
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• 2007

In this paper. we study the controllability for the semilinear fuzzy integrodifferential equations with nonlocal condition and forcing term with memory in $E_N$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_N$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.1
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• pp.25-32
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• 2011

In this paper, we study the existence and uniqueness of solutions for the impulsive semilinear fuzzy integrodifferential equations with nonlocal conditions and forcing term with memory in n-dimensional fuzzy vector space ($E^n_N$, $d_{\varepsilon}$) by using Banach fixed point theorem. That is an extension of the result of Kwun et al. [9] to impulsive system.

• Proceedings of the Jangjeon Mathematical Society
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• v.20 no.2
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• pp.183-191
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• 2017

We get one theorem that there exist solutions for the fourth order semi- linear elliptic Dirichlet boundary value problem with fully nonlinear term. We prove this result by the critical point theory and the variation of linking method.

• East Asian mathematical journal
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• v.10 no.1
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• pp.135-172
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• 1994

• Korean Journal of Mathematics
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• v.19 no.1
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• pp.65-75
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• 2011

We obtain multiplicity results for the nonlinear biharmonic problem with variable coefficient. We prove by the Leray-Schauder degree theory that the nonlinear biharmonic problem has multiple solutions for the biharmonic problem with the variable coefficient semilinear term under some conditions.

• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.627-639
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• 2013

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder's fixed point theorem. We construct the fundamental solution, establish the H$\ddot{o}$lder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions of the given equation.

• 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 the Korean Mathematical Society
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• v.38 no.4
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• pp.853-881
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• 2001

Multiplicity for doubly-periodic solutions and Dirichlet-Periodic solutions are treated.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.455-468
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• 2017

We prove the existence of multiple solutions for the fourth order nonlinear elliptic problem with fully nonlinear term. Our method is based on the critical point theory; the variation of linking method and category theory.