• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.597-608
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• 2007

We present a general uniqueness result of an endemic state for an S-I-R model with external force of infection. We reduce the problem of finding non-trivial steady state solutions to that of finding zeros of a real function of one variable so that we can easily prove the uniqueness of an endemic state. We introduce an assumption which was usually used to show stability of a non-trivial steady state. It turns out that such an assumption adopted from a stability analysis is crucial for proving the uniqueness as well, and the assumption holds for almost all cases in our model.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.327-337
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• 2015

This paper is concerned with the optimality conditions for optimal control problem of Belousov-Zhabotinskii reaction model. That is, we obtain the optimality conditions by showing the differentiability of the solution with respect to the control. We also show the uniqueness of the optimal control.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1523-1534
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• 2008

We investigate the uniqueness of transcendental analytic functions that share three values DM in one angular domain instead of the whole complex plane.

• Bulletin of the Korean Mathematical Society
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• v.54 no.3
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• pp.825-838
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• 2017

In this paper we study the uniqueness question of meromorphic functions whose certain differential polynomials share a small function.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.543-553
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• 2008

This paper is concerned with the optimal control problem of global press for an adsorbate-induced phase transition model. That is, we show the existence of the optimal control and derive the optimality conditions. Moreover, we obtain the uniqueness of the optimal control.

• East Asian mathematical journal
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• v.29 no.5
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• pp.491-501
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• 2013

This paper is concerned with the necessary conditions of the optimal boundary control for some chemotaxis equations. We obtain the existence and the necessary conditions of the optimal boundary control in the space $(H^1(0,T))^2$. Moreover, under some assumptions, we show the uniqueness of the optimal control.

• Bulletin of the Korean Mathematical Society
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• v.35 no.1
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• pp.63-74
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• 1998

Our study is dedicated to the the proof of uniqueness of solution of initially boundary value problem in Elastodynamics of initially stressed bodies with voids. This proof is obtained without recourse either to an energy conservation law or to any boundedness assumptions on the elastic coefficients.

• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.161-168
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• 2006

We prove two theorems on the uniqueness of nonlinear differential polynomials sharing 1-points, the first of which improves a recent result of Fang-Fang and Lin-Yi.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.821-828
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• 2020

In this work, we prove an existence of an inertial manifold for a system of differential equations with a non-self adjoint leading part. The result follows from the existence and uniqueness of negatively bounded solutions. In fact, we show that a sharp spectral condition is sufficient for the proof.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.497-502
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• 2022

Existence and uniqueness for fractional differential equations satisfying a general nonlocal initial or boundary condition are proven by means of Schauder's fixed point theorem. The nonlocal condition is given as an integral with respect to a signed measure, and includes the standard initial value condition and multi-point boundary value condition.