• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.827-841
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• 2022

In this paper, we study the uniqueness of two finite order transcendental meromorphic solutions f(z) and g(z) of the following complex difference equation A₁(z)f(z + 1) + A₀(z)f(z) = F(z)e^𝛼(z) when they share 0, ∞ CM, where A₁(z), A₀(z), F(z) are non-zero polynomials, 𝛼(z) is a polynomial. Our result generalizes and complements some known results given recently by Cui and Chen, Li and Chen. Examples for the precision of our result are also supplied.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.507-513
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• 2022

In this paper, we investigate some results on complex delay-differential equations of the classical Malmquist theorem. A classic illustrations of their results states us that if a complex delay equation w(t + 1) + w(t - 1) = R(t, w) with R(t, w) rational in both arguments admits (concede) a transcendental meromorphic solution of finite order, then deg_wR(t, w) ≤ 2. Development and upgrade of such results are presented in this paper. In addition, Borel exceptional zeros and poles seem to appear in special situations.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.185-196
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• 2024

In this article, we investigate the growth of meromorphic solutions of $${\alpha}(z)(\frac{{\Delta}_c{\eta}}{{\eta}})^2\,+\,(b_2(z){\eta}^2(z)\;+\;b_1(z){\eta}(z)\;+\;b_0(z))\frac{{\Delta}_c{\eta}}{{\eta}} \atop =d_4(z){\eta}^4(z)\;+\;d_3(z){\eta}^3(z)\;+\;d_2(z){\eta}^2(z)\;+\;d_1(z){\eta}(z)\;+\;d_0(z),$$ where a(z), b_i(z) for i = 0, 1, 2 and d_j (z) for j = 0, ..., 4 are given functions, △_cη = η(z + c) - η(z) with c ∈ ℂ\{0}. In particular, when the a(z), the b_i(z) and the d_j(z) are polynomials, and d₄(z) ≡ 0, we shall show that if η(z) is a transcendental entire solution of finite order, and either deg a(z) ≠ deg d₀(z) + 1, or, deg a(z) = deg d₀(z) + 1 and ρ(η) ≠ ½, then ρ(η) ≥ 1.