• Journal of the Korean Mathematical Society
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• v.30 no.2
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• pp.413-431
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• 1993

• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.421-438
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• 2015

In this paper, we study the existence of classical and generalized solutions for nonlinear differential inclusions $x^{\prime}(t){\in}F(t,x(t))$ in Hilbert spaces in which the multifunction F on the right-hand side is hemicontinuous and satisfies the semimonotone condition or is condensing. Our existence results are obtained via the selection and fixed point methods by reducing the problem to an ordinary differential equation. We first prove the existence theorem in finite dimensional spaces and then we generalize the results to the infinite dimensional separable Hilbert spaces. Then we apply the results to prove the existence of the mild solution for semilinear evolution inclusions. At last, we give an example to illustrate the results obtained in the paper.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.251-264
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• 1995

Applications of the classical Knaster-Kuratowski-Mazurkiewicz (si-mply, KKM) theorem and the fixed point theory of multifunctions defined on convex subsets of topological vector spaces have been greatly improved by adopting the concept of convex spaces due to Lassonde [L1]. In this direction, the first author [P5] found that certain coincidence theorems on a large class of composites of upper semicontinuous multifunctions imply many fundamental results in the KKM theory.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.1
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• pp.19-26
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• 2006

In this paper, using the fixed point theorem for acyclic factorizable multifunctions, we shall prove an existence theorem of general best proximity pairs and equilibrium pairs for free generalized games.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.493-519
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• 1994

In the KKM theory, there exist mutually equivalent fundamental theorems from which most of the other important results in the theory can be deduced. We give such fundamental theorems related to composites of upper semicontinuous (u.s.c.) multifunctions in a very large class.

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.319-328
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• 1999

In this paper we consider a kind of Minty`s lemma for multifunctions in Banach spaces, and apply it to obtain existence theorems for two kinds of variational-like inequalities using the KKM-Fan theorem.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.609-624
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• 1996

Recently, Giannessi [9] firstly introduced the vector-valued variational inequalities in a real Euclidean space. Later Chen et al. [5] intensively discussed vector-valued variational inequalities and vector-valued quasi variationl inequalities in Banach spaces. They [4-8] proved some existence theorems for the solutions of vector-valued variational inequalities and vector-valued quasi-variational inequalities. Lee et al. [14] established the existence theorem for the solutions of vector-valued variational inequalities for multifunctions in reflexive Banach spaces.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.1-16
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• 2013

Existence of pramarts selectors for multivalued pramart whose values are convex weakly compact subsets of a separable Banach space E (resp. subsets of a dual space $E^*$) are established. Representation theorems for multivalued pramarts are also presented.

• The Transactions of the Korean Institute of Electrical Engineers P
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• v.51 no.3
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• pp.142-148
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• 2002

Considerable progress has been made in organic photorefractive materials, since the first observation of photorefractive phenomena from organic materials. Within recent years, a large number of organic photorefractive materials, especially amorphous materials, have been developed based on polymeric composites, fully functional polymers and the multi-functional chromophore approach. Among these organic photorefractive materials, some of them containing carbazole components as a charge transporting function have been demonstrated to exhibit high performance photorefractive effects. The carbazole building blocks with charge transporting function or multifunctions play a very important role in photorefraction. In this paper, it confirmed that acceptor-substituted carbazoles show the multifunctionality both of photoconductivity and electro-optic(EO) activity and photorefractive materials newly can be developed with acceptor-substituted carbazoles.

• Proceedings of the KIEE Conference
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• 2002.06a
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• pp.120-124
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• 2002

Considerable progress has been made in organic photorefractive materials, since the first observation of photorefractive phenomena from organic materials. Within recent years, a large number of organic photorefractive materials, especially amorphous materials. have been developed based on polymeric composites, fully functional polymers and the multifunctional chromophore approach. Among these organic photorefractive materials, some of them containing carbazole components as a charge transporting function have been demonstrated to exhibit high performance photorefractive effects. The carbazole building blocks with charge transporting functionality or multifunctions play a very important role in photorefraction and have been widely used in the molecular design approach to new organic photo- refractive materials.