• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.785-795
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• 2018

In this paper, we give a uniqueness theorem on meromorphic solutions f of finite order of a class of differential-difference equations such that solutions f are uniquely determined by their poles and two distinct values.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.747-758
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• 2009

In this paper, we investigate the growth and fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives. Because of the restriction of differential equations, we obtain that the properties of fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives are more interesting than that of general transcendental meromorphic functions. Our results extend the previous results due to M. Frei, M. Ozawa, G. Gundersen, and J. K. Langley and Z. Chen and K. Shon.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1303-1314
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• 2011

We consider meromorphic solutions of q-difference equations of the form $$\sum_{j=o}^{n}a_j(z)f(q^jz)=a_{n+1}(z),$$ where $a_0(z)$, ${\ldots}$, $a_{n+1}(z)$ are meromorphic functions, $a_0(z)a_n(z)$ ≢ 0 and $q{\in}\mathbb{C}$ such that 0 < |q| ${\leq}$ 1. We give a new estimate on the upper bound for the length of the gap in the power series of entire solutions for the case 0 < |q| < 1 and n = 2. Some growth estimates for meromorphic solutions are also given in the cases 0 < |q| < 1. Moreover, we investigate zeros and poles of meromorphic solutions for the case |q| = 1.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.593-610
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• 2023

In view of Nevanlinna theory, we investigate the meromorphic solutions of q-difference differential equations and our results give the estimates about counting function and proximity function of meromorphic solutions to these equations. In addition, some interesting results are obtained for two general equations and a class of system of q-difference differential equations.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.425-441
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• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1755-1771
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• 2018

In this paper, we investigate a certain type of q-difference Riccati equation in the complex plane. We prove that q-difference Riccati equation possesses a one parameter family of meromorphic solutions if it has three distinct meromorphic solutions. Furthermore, we find that all meromorphic solutions of q-difference Riccati equation and corresponding second order linear q-difference equation can be expressed by q-gamma function if this q-difference Riccati equation admits two distinct rational solutions and $q{\in}{\mathbb{C}}$ such that 0 < ${\mid}q{\mid}$ < 1. The growth and value distribution of differences of meromorphic solutions of q-difference Riccati equation are also treated.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.473-481
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• 2021

In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic coefficients of finite logarithmic order. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.835-846
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• 2016

In this paper, we study entire solutions of some nonlinear difference equations and transcendental meromorphic solutons of some nonlinear differential equations. Our results generalize the results due to [11], [17].

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1095-1113
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• 2020

In this paper, we investigate the transcendental meromorphic solutions for the nonlinear differential equations $f^nf^{(k)}+Q_{d_*}(z,f)=R(z)e^{{\alpha}(z)}$ and fⁿf^(k) + Q_d(z, f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z), where $Q_{d_*}(z,f)$ and Q_d(z, f) are differential polynomials in f with small functions as coefficients, of degree d_* (≤ n - 1) and d (≤ n - 2) respectively, R, p₁, p₂ are non-vanishing small functions of f, and α, α₁, α₂ are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of these kinds of meromorphic solutions and their possible forms of the above equations.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1735-1748
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• 2014

In this paper, we investigate the finite order transcendental meromorphic solutions of complex difference equation of Malmquist type $$\prod_{i=1}^{n}f(z+c_i)=R(z,f)$$, where $c_1,{\ldots},c_n{\in}\mathbb{C}{\backslash}\{0\}$, and R(z, f) is an irreducible rational function in f(z) with meromorphic coefficients. We obtain some results on deficiencies of the solutions. Using these results, we prove that the growth order of the finite order solution f(z) is 1, if f(z) has Borel exceptional values $a({\in}\mathbb{C})$ and ${\infty}$. Moreover, we give the forms of f(z).