• 대한수학회지
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• 제46권4호
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• pp.691-699
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• 2009

In this paper, we establish a multiple existence result of T-periodic solutions for the semilinear parabolic boundary value problem with sublinear growth nonlinearities. We adapt sub-supersolution scheme and topological argument based on variational structure of functionals.

• 대한수학회보
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• 제36권1호
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• pp.1-13
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• 1999

Sufficient conditions for controllability of semilinear second order Volterra integrodifferential systems in Banach spaces are established using the theory of strongly continuous cosine families. The results are obtained by using the Schauder fixed point theorem. An example is provided to illustrate the theory.

• 대한수학회보
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• 제48권4호
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• pp.705-712
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• 2011

In this paper, we investigate the boundary control of semilinear neutral evolution systems with a nonlocal condition by using the Banach fixed point theorem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권1호
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• pp.1-14
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• 1998

Multiplicity results of doubly-periodic solution for semilinear heat equations having coercive nonlinearity are discussed. Our proofs rely on Mawhin's continuation theorem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권2호
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• pp.149-156
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• 2001

Sufficient conditions for boundary controllability of semilinear systems in Banach spaces are established. The results are obtained by using the analytic semigroup theory and the Banach contraction principle. An example is provided to illustrate the theory.

• 충청수학회지
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• 제23권4호
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• pp.793-800
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• 2010

We investigate the existence and uniqueness of almost automorphic mild solutions of the semilinear abstract differential equations.

• Korean Journal of Mathematics
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• 제22권4호
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• pp.633-644
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• 2014

We get one theorem that there exists a unique solution for the fourth order semilinear elliptic Dirichlet boundary value problem when the number 0 and the coefficient of the semilinear part belong to the same open interval made by two successive eigenvalues of the fourth order elliptic eigenvalue problem. We prove this result by the contraction mapping principle. We also get another theorem that there exist at least two solutions when there exist n eigenvalues of the fourth order elliptic eigenvalue problem between the coefficient of the semilinear part and the number 0. We prove this result by the critical point theory and the variation of linking method.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제6권4호
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• pp.288-292
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• 2006

Many authors have studied several concepts of fuzzy systems. Balasubramaniam and Muralisankar (2004) proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. Recently, Park, Park and Kwun (2006) find the sufficient condition of nonlocal controllability for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. In this paper, we study the existence and uniqueness of solutions 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 $E_{N}$.

• 호남수학학술지
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• 제20권1호
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• pp.67-78
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• 1998

• 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.