• Bulletin of the Korean Mathematical Society
• /
• v.47 no.4
• /
• pp.751-765
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.2
• /
• pp.371-385
• /
• 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.

• Honam Mathematical Journal
• /
• v.29 no.4
• /
• pp.695-700
• /
• 2007

We establish two uniqueness theorems for non-constant entire functions which extends results of J. S. Hwang in J. Math. Anal. and its Appl. Vol. 37 (1972) 452-456.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.631-640
• /
• 2007

The purpose of this article is to deal with the multiple values and uniqueness of meromorphic functions with small functions in the whole complex plane. We obtain a more general theorem which improves and extends strongly the results of R. Nevanlinna, Li-Qiao, Yao, Yi, and Thai-Tan.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.623-629
• /
• 2007

In this paper, we study the uniqueness of entire functions and prove the following result: Let f and g be two nonconstant entire functions, n, m be positive integers. If $f^n(f^m-1)f#\;and\;g^n(g^m-1)g#$ share 1 IM and n>4m+11, then $f{\equiv}g$. The result improves the result of Fang-Fang.

• Journal of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.781-791
• /
• 2001

We consider the inverse conductivity problem to identify the unknown conductivity $textsc{k}$ as well as the domain D. We show hat, unlike the case when $textsc{k}$ is known, even a two or three dimensional ball may not be identified uniquely if the conductivity constant $textsc{k}$ is not known. We find a necessary and sufficient condition on the Cauchy data (u│∂Ω, g) for the uniqueness in identification of $textsc{k}$ and D. We also discuss on failure of stability.

• Communications of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.171-177
• /
• 2018

In this research paper considering a differential equation with impulsive effect and dependent delay and applied Banach fixed point theorem using the impulsive condition to the impulsive fractional functional differential equation of an order ${\alpha}{\in}(1,2)$ to get an uniqueness solution. At last, theorem is verified by using a numerical example to illustrate the uniqueness solution.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.3
• /
• pp.789-799
• /
• 2019

In this paper, we deal with unicity of a nonconstant zero-order meromorphic function f(z) and its shift f(qz) when they share four distinct values IM or share three distinct values with multiplicities truncated to level 4 in the extended complex plane, where $q{\in}\mathbb{C}{\setminus}\{0\}$. We also give an uniqueness result for f(z) sharing sets with its shift.

• Communications of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.525-545
• /
• 2023

In the paper, we have exhaustively studied about the uniqueness of meromorphic function sharing two small functions with its k-th derivative as these types of results have never been studied earlier. We have obtained a series of results which will improve and extend some recent results of Banerjee-Maity [1].

• Communications of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.105-116
• /
• 2024

In this paper, we prove a uniqueness theorem of non-constant meromorphic functions of hyper-order less than 1 sharing two values CM and two partial shared values IM with their shifts. Our result in this paper improves and extends the corresponding results from Chen-Lin [2], Charak-Korhonen-Kumar [1], Heittokangas-Korhonen-Laine-Rieppo-Zhang [9] and Li-Yi [12]. Some examples are provided to show that some assumptions of the main result of the paper are necessary.