Kyungpook Mathematical Journal

  • 제64권1호
  • /
  • Pages.185-196
  • /
  • 2024
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On the Growth of Transcendental Meromorphic Solutions of Certain algebraic Difference Equations

  • Xinjun Yao (Department of Mathematics, Shaoxing College of Arts and Sciences) ;
  • Yong Liu (Department of Mathematics, Shaoxing College of Arts and Sciences) ;
  • Chaofeng Gao (Department of Mathematics, Shaoxing College of Arts and Sciences)
  • 투고 : 2023.03.08
  • 심사 : 2023.06.27
  • 발행 : 2024.03.31
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초록

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), bi(z) for i = 0, 1, 2 and dj (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 bi(z) and the dj(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.

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과제정보

The authors would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions.

참고문헌

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