• 제목/요약/키워드: Borel exceptional values

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COMPLEX DELAY-DIFFERENTIAL EQUATIONS OF MALMQUIST TYPE

  • NAGASWARA, P.;RAJESHWARI, S.
    • Journal of applied mathematics & informatics
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    • 제40권3_4호
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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 degwR(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.

SHARED VALUES AND BOREL EXCEPTIONAL VALUES FOR HIGH ORDER DIFFERENCE OPERATORS

  • Liao, Liangwen;Zhang, Jie
    • 대한수학회보
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    • 제53권1호
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    • pp.49-60
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    • 2016
  • In this paper, we investigate the high order difference counterpart of $Br{\ddot{u}}ck^{\prime}s$ conjecture, and we prove one result that for a transcendental entire function f of finite order, which has a Borel exceptional function a whose order is less than one, if ${\Delta}^nf$ and f share one small function d other than a CM, then f must be form of $f(z)=a+ce^{{\beta}z}$, where c and ${\beta}$ are two nonzero constants such that $\frac{d-{\Delta}^na}{d-a}=(e^{\beta}-1)^n$. This result extends Chen's result from the case of ${\sigma}(d)$ < 1 to the general case of ${\sigma}(d)$ < ${\sigma}(f)$.

MEROMORPHIC SOLUTIONS OF A COMPLEX DIFFERENCE EQUATION OF MALMQUIST TYPE

  • Zhang, Ran-Ran;Huang, Zhi-Bo
    • 대한수학회보
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    • 제51권6호
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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).