• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.431-450
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• 2016

In this paper, the existence, uniqueness, stability via continuous dependence and Ulam stabilities of nonlinear integro-differential equations with random impulses are studied under sufficient condition. The results are obtained by using Leray-Schauder alternative fixed point theorem and Banach contraction principle.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.513-524
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• 2022

In this paper, we introduce the notion of tensor product in groups and prove its existence and uniqueness. Next, we provide the Isbell's zigzag theorem for dominions in commutative groups. We then show that in the category of commutative groups dominions are trivial. This enables us to deduce a well known result epis are surjective in the category of commutative groups.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.571-592
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• 2022

By established a Banach space with the Hausdorff distance, we introduce the alternative fixed-point theorem to explore the existence and uniqueness of a fixed subset of Y and investigate the stability of set-valued Euler-Lagrange functional equations in this space. Some properties of the Hausdorff distance are furthermore explored by a short and simple way.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.205-226
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• 2018

In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n({\mathbb{C}})$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the p-Casorati determinant with $p{\in}{\mathbb{C}}^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition "order=0". The results obtained include p-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.899-911
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• 2018

In this paper, we consider the second-order nonlinear differential equation with the nonlocal boundary conditions. We first reformulate this boundary value problem as a fixed point problem for a Fredholm integral equation operator, and then present a result on the existence and uniqueness of the solution by using the contraction mapping theorem. Furthermore, we establish a sufficient condition on the functions ${\mu}$ and $h_i$, i = 1, 2 that guarantee a unique solution for this nonlocal problem in a Hilbert space. Also, accurate analytic solutions in series forms for this boundary value problems are obtained by the Adomian decomposition method (ADM).

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.865-870
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• 2018

We show that if two nonconstant meromorphic functions f and g on $\mathbb{C}$ sharing some finite sets IM, then there is a nonconstant rational function R(z) such that R(f) = R(g).

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.785-795
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• 2018

In this paper, we give a uniqueness theorem on meromorphic solutions f of finite order of a class of differential-difference equations such that solutions f are uniquely determined by their poles and two distinct values.

• The Pure and Applied Mathematics
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• v.10 no.1
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• pp.13-23
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• 2003

The purpose of this paper is to prove the fundamental existence and uniqueness theorems for lightlike curves in a 6-dimensional semi-Euclidean space Rq of index q, since the general n-dimensional cases are too complicated.

• Honam Mathematical Journal
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• v.37 no.1
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• pp.99-112
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• 2015

In this paper we consider the periodic Cauchy problem for the generalized two-component Hunter-Saxton system with analytic initial data and we prove a Cauchy-Kowalevski type theorem for the generalized two-component Hunter-Saxton system, that establishes the existence and uniqueness of real analytic solutions.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.351-355
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• 2019

We obtain two characterizations of uniform distribution based on ratios of upper record values by the properties of independence and identical distribution.