• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권2호
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• pp.81-97
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• 1999

This paper deals with the time optimal control problem for the retarded semilinear system by using the construction of fundamental solution in case where the principal operators are unbounded operators.

• Korean Journal of Mathematics
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• 제18권1호
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• pp.87-96
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• 2010

We consider the semilinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the semilinear biharmonic boundary value problem. We show this result by using the critical point theory, the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

• 대한수학회지
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• 제39권5호
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• pp.775-782
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• 2002

In this paper we prove the existence of mild soultions for semilinear differential equations in a Banach space. The results are obtained by using the semigroup theory and the Schaefer fixed point theorem. An example is provided to illustrate the theory.

• 대한수학회보
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• 제55권1호
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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.

• 한국지능시스템학회:학술대회논문집
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• 한국지능시스템학회 2008년도 춘계학술대회 학술발표회 논문집
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• pp.26-28
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• 2008

This paper is to investigate the existence theorem for the semilinear fuzzy integrodifferential equation in ${E_N}$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in ${E_N}$. Main tool is successive iteration method.

• East Asian mathematical journal
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• 제30권3호
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• pp.327-334
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• 2014

In this paper, we construct extrapolated expanded mixed finite element approximations to approximate the scalar unknown, its gradient and its flux of semilinear Sobolev equations. To avoid the difficulty of solving the system of nonlinear equations, we use an extrapolated technique in our construction of the approximations. Some numerical examples are used to show the efficiency of our schemes.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권4호
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• pp.339-342
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• 2009

In this paper, we investigate the existence and uniqueness of fuzzy solutions for semilinear fuzzy integrodifferential equations using integral contractor. The notion of 'bounded integral contractor', introduced by Altman[1], is weaker than Lipschitz condition.

• 한국지능시스템학회논문지
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• 제18권4호
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• pp.543-548
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• 2008

This paper is to investigate the existence theorem for the semilinear fuzzy integrodifferential equation in $E_N$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_N$. Main tool is successive iteration method.

• 충청수학회지
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• 제28권3호
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• pp.365-375
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• 2015

Of concern is the existence, uniqueness, and continuous dependence of a mild solution of a nonlocal Cauchy problem for a semilinear mixed Volterra-Fredholm functional integrodifferential equation. Our analysis is based on the theory of a strongly continuous semigroup of operators and the Banach fixed point theorem.

• 대한수학회논문집
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• 제37권2호
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• pp.423-443
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• 2022

We study the existence and long-time behavior of weak solutions to a class of strongly degenerate semilinear parabolic equations with exponential nonlinearities on ℝ^N. To overcome some significant difficulty caused by the lack of compactness of the embeddings, the existence of a global attractor is proved by combining the tail estimates method and the asymptotic a priori estimate method.