• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.203-215
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• 2009

In this article, we study the existence and uniqueness of mild and classical solutions for a nonlinear impulsive differential equation with nonlocal conditions u'(t) = Au(t) + f(t, u(t); Tu(t); Su(t)), $0{\leq}t{\leq}T_0$, $t{\neq}t_i$, u(0) + g(u) = $u_0$, ${\Delta}u(t_i)=I_i(u(t_i))$, i = 1,2,${\ldots}$p, 0<$t_1$<$t_2$<$\cdots$<$t_p$<$T_0$, in a Banach space X, where A is the infinitesimal generator of a $C_0$ semigroup, g constitutes a nonlocal conditions, and ${\Delta}u(t_i)=u(t_i^+)-u(t_i^-)$ represents an impulsive conditions.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.221-236
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• 1997

In this paper we investigate the multiplicity of positive solutions to a quasilinear Neumann problem; $$ {\varepsilon^m div($\mid$\bigtriangledown_u$\mid$^{m-2}\bigtriangledown_u) - u$\mid$u$\mid$^{m-2} + u$\mid$u$\mid$^{m-2} + u$\mid$u$\mid$^{p-2} = 0 in \omega $$ $$ \frac{\partial u}{\partial \nu} = 0 on \partial \omega, $$ making use of Ljusternik Schnirelmann category theory.

• Journal of the Korean Mathematical Society
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• v.57 no.6
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• pp.1551-1571
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• 2020

This paper is concerned with the following Kirchhoff-Schrödinger-Poisson system $$\begin{cases} -(a+b{\displaystyle\smashmargin{2}\int\nolimits_{\mathbb{R}^3}}{\mid}{\nabla}u{\mid}^2dx){\Delta}u+V(x)u+{\mu}{\phi}u={\lambda}f(x){\mid}u{\mid}^{p-2}u+g(x){\mid}u{\mid}^{p-2}u,&{\text{ in }}{\mathbb{R}}^3,\\-{\Delta}{\phi}={\mu}{\mid}u{\mid}^2,&{\text{ in }}{\mathbb{R}}^3, \end{cases}$$ where a > 0, b, µ ≥ 0, p ∈ (1, 2), q ∈ [4, 6) and λ > 0 is a parameter. Under some suitable assumptions on V (x), f(x) and g(x), we prove that the above system has at least two different nontrivial solutions via the Ekeland's variational principle and the Mountain Pass Theorem in critical point theory. Some recent results from the literature are improved and extended.

• Journal of the Korean Association of Geographic Information Studies
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• v.11 no.2
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• pp.132-147
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• 2008

So far ubiquitous service (u-service) priority has seldom been empirically examined based on the customer's view. It is usual to prioritize the relative importance of u-service variables by the supplier's intuition and a few specialist's experienced knowledge. Such approaches have the disadvantage that they provide only limited empirical information on the field practices in relation to u-service since customer demand of u-service is poorly defined despite abundant interest in this problem. Therefore, the aim of this research was to develop u-service priority model in the context of multi-criteria framework integrating customer and supplier's view, using high technology acceptance theory as major controlling factors. An important question was how to measure or represent criteria that is important to u-service and should be included in a priority model. The selection criteria for the model variables were derived from high technology acceptance theory and AHP approach through the analysis of frequency count, elimination of overlapping factors and brainstorming with specialists. Daegu showed top-rankings in transportation-aid service, guidance service for the eyesight disabled and u-telematics service. In contrast, disaster prevention service and industrial specialized town service ranked highly in the typical supplier's approach were not a dominant determining factor in the u-service priority. The model identified the fact that typical high priority service in terms of supplier's view did not necessarily accompany the important predictor for the u-service priority.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.731-737
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• 2004

We investigate change of the tensor ${U^{v}}_{\omega\mu}$ induced by the conformal change in 7-dimensional g-unified field theory. These topics will be studied for the second class with the first category in 7-dimensional case.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.139-144
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• 1995

Two subgroups U and V of a finite group G are called to be p-conjugate for a prime p if a Sylow p-subgroup of U is conjugate to a Sylow p-subgroup of V. This concept of p-conjugacy also makes sense for some infinite groups with a reasonable Sylow theory.

• Korean Journal of Mathematics
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• v.12 no.2
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• pp.185-191
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• 2004

We investigate change of the vector $U_{\mu}$ induced by the conformal change in 5-dimensional $g$-unified field theory. These topics will be studied for the second class in 5-dimensional case.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.141-149
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• 1997

We investigate chnage of the tensor $U^{\nu}{_{\lambda}{\mu}}$ induced by the conformal change in 6-dimensional $g$-unified field theory. These topics will be studied for the second class with the second category in 6-dimensional case.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.199-205
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• 1999

We investigate change of the tensor $U^{\nu}_{{\lambda}{\mu}}$ induced by the conformal change in 5-dimensional $g$-unified field theory. These topics will be studied for the second class in 5-dimensional case.

• East Asian mathematical journal
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• v.38 no.1
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• pp.33-41
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• 2022

In this paper, we study singular Dirichlet boundary value problems involving ϕ-Laplacian. Using fixed point index theory, the existence of positive solutions is established under the assumption that the nonlinearity f = f(u) has a positive falling zero and is either superlinear or sublinear at u = 0.