• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.203-211
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• 2005

If a meromorphic solution of second order homogeneous linear differential equation is factorizable, then the right factor of the factorization of the solution has order not more than the coefficient's. And some asympotic properties of solutions are studied.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.597-610
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• 2024

Using the Nevanlinna value distribution theory of algebroid functions, this paper investigates the growth of two types of complex algebraic differential equation with algebroid solutions and obtains two results, which extend the growth of complex algebraic differential equation with meromorphic solutions obtained by Gao [4].

• 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.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.39-50
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• 2018

In this paper, we deal with the uniqueness problem for the power of p-adic meromorphic functions. The results obtained in this paper are the p-adic analogues and supplements of the theorems given by Yang and Zhang [Non-existence of meromorphic solution of a Fermat type functional equation, Aequationes Math. 76(2008), 140-150], Chen, Chen and Li [Uniqueness of difference operators of meromorphic functions, J. Ineq. Appl. 2012(2012), Art 48], Zhang [Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl. 367(2010), 401-408].

• Bulletin of the Korean Mathematical Society
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• v.61 no.3
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• pp.745-762
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• 2024

In this paper, we study the existence of finite order meromorphic solutions of the following non-linear difference equation fⁿ(z) + P_d(z, f) = p₁e^α1z + p₂e^α2z + p₃e^α3z, where n ≥ 2 is an integer, P_d(z, f) is a difference polynomial in f of degree d ≤ n - 2 with small functions of f as its coefficients, p_j (j = 1, 2, 3) are small meromorphic functions of f and α_j (j = 1, 2, 3) are three distinct non-zero constants. We give the expressions of finite order meromorphic solutions of the above equation under some restrictions on α_j (j = 1, 2, 3). Some examples are given to illustrate the accuracy of the conditions.

• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1181-1203
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• 2018

In this paper, we are mainly devoted to find out the general meromorphic solution of some specific type of differential equation. We have also answered an open question posed by Banerjee-Chakraborty [4] by extending their results in a large extent. We have provided an example showing that the conclusion of the results of Zhang-Yang [16] is not general true. Some examples have been exhibited to show that certain claims are true in our main result. Finally some questions have been posed for the future research in this direction.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.597-607
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• 2019

In this article, we consider properties of transcendental meromorphic solutions of the complex differential-difference equation $$P_n(z)f^{(n)}(2+{\eta}_n)+{\cdots}+P_1(z)f^{\prime}(z+{\eta}_1)+P_0(z)f(z+{\eta}_0)=0$$, and its non-homogeneous equation. Our results extend earlier results by Liu et al. [9].

• Bulletin of the Korean Mathematical Society
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• v.40 no.2
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• pp.235-241
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• 2003

It is proved that the product of any two linearly independent meromorphic solutions of second order linear differential equations with coefficients of small lower growth must have infinite exponent of convergence of its zero-sequences, under some suitable conditions.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.229-246
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• 2024

We consider the delay differential equations $$b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z, w(z))}{Q(z, w(z))}$$, where k ∈ {1, 2}, a(z), b(z) ≢ 0, c(z) ≢ 0 are rational functions, and P(z, w(z)) and Q(z, w(z)) are polynomials in w(z) with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution w with hyper-order ρ2(w) < 1, then either deg_w(P) = deg_w(Q) + 1 ≤ 3 or max{deg_w(P), deg_w(Q)} ≤ 1. In addition, it is shown that in the case max{deg_w(P), deg_w(Q)} = 0 the equations above can have such a solution, with an additional zero density requirement, only if the coefficients of the equation satisfy certain strict conditions.