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The growth of linear differential equations and their applications

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Abstract

In this paper, we investigate the growth properties of solutions of linear complex differential equation and give some applications in the growth estimates of entire functions that share one finite value with one of their derivatives.

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References

  1. Z. X. Chen and C. C. Yang,Some further results on the zeros and growths of entire solutions of second order linear differential equations, Kodai Mathematical Journal22 (1999), 273–285.

    Article  MATH  MathSciNet  Google Scholar 

  2. G. Gundersen,Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, Journal of the London Mathematical Society37 (2) (1988), 88–104.

    Article  MATH  MathSciNet  Google Scholar 

  3. W. K. Hayman,Meromorphic Functions, Clarendon Press, Oxford, 1964.

    MATH  Google Scholar 

  4. W. K. Hayman,The local growth of power series: a survey of the Wiman-Valiron method, Canadian Mathematical Bulletin17 (1974), 317–358.

    MATH  MathSciNet  Google Scholar 

  5. K. H. Kwon,On the growth of entire functions satisfying second order linear differential equations, Bulletin of the Korean Mathematical Society33 (3) (1996), 487–496.

    MATH  MathSciNet  Google Scholar 

  6. I. Laine,Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin-New York, 1993.

    Google Scholar 

  7. G. Valiron,Lectures on the General Theory of Integral Functions, Chelsea, New York, 1949.

    Google Scholar 

  8. J. P. Wang and H. X. Yi,Entire functions that have the same fixed points with their first derivatives, Journal of Mathematical Analysis and Applications290 (2004), 235–246.

    Article  MATH  MathSciNet  Google Scholar 

  9. L. Yang,Value Distribution Theory, Springer-Verlag, Berlin, 1993.

    MATH  Google Scholar 

  10. L. Z. Yang,Solution of a differential equation and its applications, Kodai Mathematical Journal22 (1999), 458–464.

    Article  MATH  MathSciNet  Google Scholar 

  11. L. Z. Yang,Entire functions that share one value with one of their derivatives, inFinite or Infinite Dimensional Complex Analysis, Fukuoka 1999 (Proceedings of a Conference), Lecture Notes in Pure and Applied Mathematics, Vol. 214, Marcel Dekker, New York, 2000, pp. 617–624.

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Shandong University, 250100, Jinan, Shandong, P.R. China

    Lian-Zhong Yang

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  1. Lian-Zhong Yang
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Additional information

This work was supported by the NNSF of China (No. 10371065) and the NSF of Shandong Province, China (No. Z2002A01).

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Yang, LZ. The growth of linear differential equations and their applications. Isr. J. Math. 147, 359–370 (2005). https://doi.org/10.1007/BF02785372

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  • DOI: https://doi.org/10.1007/BF02785372

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