• 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].

• 충청수학회지
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• 제21권1호
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• pp.139-146
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• 2008

We investigate the uniqueness and multiplicity of solutions for the nonlinear elliptic system with Dirichlet boundary condition $$\{-{\Delta}u+g_1(u,v)=f_1(x){\text{ in }}{\Omega},\\-{\Delta}v+g_2(u,v)=f_2(x){\text{ in }}{\Omega},$$ where ${\Omega}$ is a bounded set in $R^n$ with smooth boundary ${\partial}{\Omega}$. Here $g_1$, $g_2$ are nonlinear functions of u, v and $f_1$, $f_2$ are source terms.

• 대한수학회보
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• 제59권5호
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• pp.1105-1117
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• 2022

In this paper, we obtain a second main theorem for holomorphic curves and moving hyperplanes of Pⁿ(C) where the counting functions are truncated multiplicity and have different weights. As its application, we prove a uniqueness theorem for holomorphic curves of finite growth index sharing moving hyperplanes with different multiple values.

• 대한수학회보
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• 제41권3호
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• pp.483-492
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• 2004

Let : [0, 1] $\times$ [0, $\infty$) $\longrightarrow$ [0, $\infty$) be continuous and a ${\in}$ C([0, 1], [0, $\infty$)),and let ${\xi}_{i}$ $\in$ (0, 1) with 0 < {\xi}$_1$ < ${\xi}_2$ < … < ${\xi}_{m-2}$ < 1, $a_{i}$, $b_{i}$ ${\in}$ [0, $\infty$) with 0 < $\Sigma_{i=1}$ /$^{m-2}$ $a_{i}$ < 1 and $\Sigma_{i=1}$$^{m-2}$ < l. This paper is concerned with the following m-point boundary value problem: $\chi$″(t)＋a(t) (t.$\chi$(t))＝0,t ${\in}$(0,1), $\chi$'(0)＝$\Sigma_{i=1}$ $^{m-2}$ /$b_{i}$$\chi$'(${\xi}_{i}$),$\chi$(1)＝$\Sigma_{i=1}$$^{m-2}$$a_{i}$$\chi$(${\xi}_{i}$). The existence, multiplicity and uniqueness of positive solutions of this problem are discussed with the help of two fixed point theorems in cones, respectively.

• 대한수학회보
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• 제23권2호
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• pp.197-197
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• 1986

• 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.

• East Asian mathematical journal
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• 제40권1호
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• pp.37-50
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• 2024

We establish the existence, multiplicity and uniqueness of positive solutions to nonlocal boundary value systems with strongly coupled integral boundary condition by using the global continuation theorem and Banach's contraction principle.

• Korean Journal of Mathematics
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• 제23권4호
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• pp.619-630
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• 2015

This paper is devoted to investigate the multiple solutions for a class of the cooperative elliptic system involving subcritical Sobolev exponents on the bounded domain with smooth boundary. We first show the uniqueness and the negativity of the solution for the linear system of the problem via the direct calculation. We next use the variational method and the mountain pass theorem in the critical point theory.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권3호
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• pp.161-169
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• 2008

We investigate the existence of solutions u(x, t) for perturbations of the elliptic system with Dirichlet boundary condition $$\array {L{\xi}+{\mu}g({\xi}+2{\eta})=f\;in\;{\Omega}}\\{L{\eta}+{\nu}g({\xi}+2{\eta})=f\;in\;{\Omega}}$$ (0.1) where $g(u)=Bu^+-Au^-$, $u^+=max\{u,\;0\}$, $u^-=max\{-u,\;0\}$, ${\mu}$, ${\nu}$ are nonzero constants and the nonlinearity $({\mu}+2{\nu})g(u)$ crosses the eigenvalues of the elliptic operator L.

• 대한수학회보
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• 제55권1호
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• pp.205-226
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• 2018

In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of ${\mathbb{C}}^m$ into ${\mathbb{P}}^n({\mathbb{C}})$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the p-Casorati determinant with $p{\in}{\mathbb{C}}^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition "order=0". The results obtained include p-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.