• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.509-517
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• 2005

We shall prove the existence and uniqueness theorem of a solution to the non local fuzzy differential equation using the contraction mapping principle.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권2호
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• pp.115-127
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• 2000

The purpose of this paper is to prove the fundamental existence and uniqueness theorems of null curves in semi-Riemannian manifolds M of index 2.

• 대한수학회논문집
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• 제13권3호
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• pp.515-523
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• 1998

We generalize the uniqueness theorem of K.Yoneda[9] for nonharmonic series under a much weaker condition as follows: Let ｛λ$_{k}$ ｝$_{k}$ =$o^{\infty}$ be a discrete sequence in $R^n$. If (equation omitted) = 0 for all x $\in$ $R^n$ and there exists a number N > 0 such that (equation omitted) then$ a_{k}$ = 0 for all k $\in$ $N_{0}$.

• 대한수학회보
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• 제57권5호
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• pp.1307-1317
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• 2020

Let f be a nonconstant meromorphic function of hyper order strictly less than 1, and let c be a nonzero finite complex number such that f(z + c) ≢ f(z). We prove that if ∆_cf = f(z + c) - f(z) and f share 0, ∞ CM and 1 IM, then ∆_cf = f. Our result generalizes and greatly improves the related results.

• 대한수학회보
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• 제52권5호
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• pp.1401-1422
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• 2015

Under the restriction of finite order, we prove two uniqueness theorems of nonconstant meromorphic functions sharing three values with their difference operators, which are counterparts of Theorem 2.1 in [6] for a finite-order meromorphic function and its shift operator.

• East Asian mathematical journal
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• 제24권1호
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• pp.111-123
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• 2008

In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

• Kyungpook Mathematical Journal
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• 제51권2호
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• pp.195-204
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• 2011

We prove a uniqueness theorem for meromorphic functions sharing three weighted values, which improves a result given by N. Terglane in 1989 and a result given by X. M. Li and H. X. Yi in 2003. Some examples are provided to show that the result of the paper is best possible.

• 대한수학회논문집
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• 제36권4호
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• pp.729-741
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• 2021

We mainly study the value distributions of L-functions in the extended selberg class. Concerning weighted sharing, we prove an uniqueness theorem when certain differential monomial of a meromorphic function share a polynomial with certain differential monomial of an L-function which improve and generalize some recent results due to Liu, Li and Yi [11], Hao and Chen [3] and Mandal and Datta [12].

• Journal of applied mathematics & informatics
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• 제37권5_6호
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• pp.491-506
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• 2019

In this paper, we show the existence and uniqueness of solution to stochastic differential equations under weakened $H{\ddot{o}}lder$ condition and a weakened linear growth condition. Furthermore, the properties of their solutions investigated and estimate for the error between Picard iterations $x_n(t)$ and the unique solution x(t) of SDEs.

• 대한수학회지
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• 제58권5호
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• pp.1261-1277
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• 2021

An inertial manifold is often constructed as a graph of a function from low Fourier modes to high ones and one used to consider backward bounded (in time) solutions for that purpose. We here show that the proof of the uniqueness of such solutions is crucial in the existence theory of inertial manifolds. Avoiding contraction principle, we mainly apply the Arzela-Ascoli theorem and Laplace transform to prove their existence and uniqueness respectively. A non-self adjoint example is included, which is related to a differential system arising after Kwak transform for Navier-Stokes equations.