• 대한수학회논문집
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• 제32권4호
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• pp.1025-1031
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• 2017

We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.185-199
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• 2003

In this paper, we apply finite element Galerkin method to a single-phase quasi-linear Stefan problem with a forcing term. We consider the existence and uniqueness of a semidiscrete approximation and optimal error estimates in $L_2$, $L_{\infty}$, $H_1$ and $H_2$ norms for semidiscrete Galerkin approximations we derived.

• 대한수학회보
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• 제55권3호
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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).

• 한국지능시스템학회논문지
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• 제2권1호
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• pp.3-16
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• 1992

In this paper, we establish the conceptes of compactifications of a L-fuzzy topological space and a order relation in these compactifications. This order is a preorder. The existemce problem and the uniqueness problem of the largest compactifications are closely related to the mapping extension problem. We give out the largest compactifications and show the non-uniqueness of the largest compactifications in the preorder for a kind of spaces. Moreover, under some natural assumptions of separation axioms, we prove that the preorder is just a partial order, thus it ensures the uniqueness of the largest compactification. In addition. the related discussion involves the special properties of fuzzy product space, the latter seems to be independent interesting.

• 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.

• 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.

• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.1-9
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• 2017

In this paper, we investigate the uniqueness problem related to the power of a meromorphic functions sharing a small function with its derivative. The results in this paper improve and generalize some well known previous results.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.247-263
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• 2023

In this article, we investigate the uniqueness problem of q-shift difference polynomial of meromorphic (entire) function with zero-order. Consequently, we prove three results with significantly generalize the results of Goutam Haldar.

• 한국해양공학회지
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• 제17권5호
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• pp.19-24
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• 2003

The question of wave source identification in a wave maker problem is the primary objective of the this paper. With the observed wave elevation, the existence of the wave maker velocity is discussed with the help of the mathematical theory of inverse problems. Utilizing the property of the Strum-Liouville system and compactness, the uniqueness and the ill-posedness(in the sense of stability) for the identification are proved.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권3호
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• pp.179-191
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• 2005

In this paper we consider a Dirichlet problem in the unit disk. We show that the equation has a unique or multiple solutions according to the range of the parameter. Moreover, we prove that the equation admits a nonradial bifurcation at each branch of radial solutions.