• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.513-522
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• 2013

This paper mainly deals with the stochastic control system, the existence and uniqueness of solutions and the behavior of solutions are investigated. Firstly, we obtain sufficient conditions which guarantee the existence and uniqueness of solutions to the stochastic control system. And then, boundedness of the solution to the system is achieved under mean-square linear growth condition.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1007-1019
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• 2000

In this paper, we discuss a uniqueness problem for the Cauchy problem of the Euler equation. W give a sufficient condition on the vorticity to show the uniqueness of a class of generalized solution in terms of the generalized solution in terms o the generalized Besov space. The condition allows the iterated logarithmic singularity to the vorticity of the solution. We also discuss the break down (or blow up) condition for a smooth solution to the Euler equation under the related assumption.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1157-1171
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• 2013

In this paper, by using the $q$-difference analogue of lemma on the logarithmic derivative lemma to re-establish some estimates of Nevanlinna characteristics of $f(qz)$, we deal with the value distribution and uniqueness of certain types of $q$-difference polynomials.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.717-731
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• 2022

We introduce the notion of quasi-roots and study their uniqueness in right-angled Artin groups.

• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.145-164
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• 2011

In the paper, we study with weighted sharing method the uniqueness of entire functions concerning nonlinear differential polynomials sharing one value and prove two uniqueness theorems, first one of which generalizes some recent results in [10] and [16]. Our second theorem will supplement a result in [17].

• Bulletin of the Korean Mathematical Society
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• v.41 no.1
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• pp.109-116
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• 2004

In this paper, we study the uniqueness of entire functions and prove the following result: Let f(z) and g(z) be two nonconstant entire functions, $n\;{\geq}\;7$ a positive integer, and let a be a nonzero finite complex number. If $f^{n}(z)(f(z)\;-\;1)f'(z)\;and\;g^{n}(z)(g(z)\;-\;1)g'(z)$ share a CM, then $f(z)\;{\equiv}\;g(z)$. The result improves the theorem due to ref. [3].

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.13-33
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• 2015

In this paper, we study the uniqueness problems of entire or meromorphic functions concerning differential polynomials that share one value with multiplicity using weighted sharing method. We prove two main theorems which generalize and improve the results of Fang and Fang [2], Dyavanal [1] and others and also solve the open problem posed by Dyavanal. This method yields some new results.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.175-187
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• 2002

The existence and uniqueness of steady states for the age structured S-I-R epidemic model is considered. Intercohort form with external force is considered for the force of infection. Existence is obtained for nonvanishing external force of infection. Uniqueness is shown for the case where there is no vertical transmission of the disease.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.785-802
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• 1995

It is well known that every periodic function $f \in L^p([0,2\pi]), p > 1$, can be represented by a convergent trigonometric series called the Fourier series of f. Uniqueness of the representing series is very important, and we know that the Fourier series of a periodic function $f \in L^p([0,2\pi])$ is unique.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1047-1061
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• 2011

In this paper, a class of second-order boundary value problems with Sturm-Liouville boundary conditions or multi-point conditions is considered. Some existence and uniqueness theorems of positive solutions of the problem are obtained by using monotone iterative technique, the iterative sequences yielding approximate solutions are also given. The results are illustrated with an example.