• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권1호
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• pp.19-30
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• 2002

We consider one class of bursting oscillation models, that is square-wave burster. One of the interesting features of these models is that periodic bursting solution need not to be unique or stable for arbitrarily small values of a singular perturbation parameter $\epsilon$. Recent results show that the bursting solution is uniquely determined and stable for most of the ranges of the small parameter $\epsilon$. In this paper, we present a condition of uniqueness and stability of periodic bursting solutions for all sufficiently small values of $\epsilon$ > 0.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.877-894
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• 2013

In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green's function, a nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem in a cone. Some examples are included to show the applicability of our results.

• 대한수학회보
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• 제52권1호
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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.

• Journal of applied mathematics & informatics
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• 제35권5_6호
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• pp.529-542
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• 2017

In this paper, using the notion of weakly weighted sharing and relaxed weighted sharing, we investigate the uniqueness problems of certain differential polynomials sharing a small function. The results obtained in this paper extend the theorem obtained by Jianren Long [9].

• 대한수학회논문집
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• 제17권1호
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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.

• 대한수학회지
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• 제32권4호
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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.

• 대한수학회보
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• 제48권5호
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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.

• 대한수학회보
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• 제47권4호
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• pp.751-765
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• 2010

In this paper, we deal with a uniqueness theorem of two nonconstant meromorphic functions that share three values and one pair of polynomials. The results in this paper improve those given by G. G. Gundersen, G. Brosch and other authors.

• 대한수학회보
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• 제50권4호
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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.

• 대한수학회보
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• 제41권2호
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• pp.371-385
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• 2004

In this paper, we investigate the uniqueness of positive solutions to weak competition models with self-cross diffusion rates under homogeneous Dirichlet boundary conditions. The methods employed are upper-lower solution technique and the variational characterization of eigenvalues.