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On subnormal solutions of second order linear periodic differential equations

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Abstract

In this paper, we investigate the existence and the form of subnormal solution for a class of second order periodic linear differential equations, estimate the growth properties of all solutions, and answer the question raised by Gundersen and Steinbart.

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References

  1. Yang L. Value Distribution Theory and New Research (in Chinese). Beijing: Science Press, 1982

    Google Scholar 

  2. Hayman W. Meromorphic Function. Oxford: Clarendon Press, 1964

    Google Scholar 

  3. Laine I. Nevanlinna Theory and Complex Differential Equations. Berlin: W de Gruyter, 1993

    Google Scholar 

  4. Yi H X, Yang C C. The Uniqueness Theory of Meromorphic Functions (in Chinese). Beijing: Science Press, 1995

    Google Scholar 

  5. Gundersen G, Steinbart M. Subnormal solutions of second order linear differential equations with periodic coefficients. Results in Math, 25: 270–289 (1994)

    MATH  MathSciNet  Google Scholar 

  6. Wittich H. Subnormale Lösungen der differentialgleichung w″ + p(e z)w′ + q(e z)w = 0. Nagoya Math J, 30: 29–37 (1967)

    MATH  MathSciNet  Google Scholar 

  7. Chiang Y M, Gao S A. On a problem in complex oscillation theory of periodic second order linear differential equations and some related perturbation results. Ann Acad Sci Fenn Math, 27: 273–290 (2002)

    MATH  MathSciNet  Google Scholar 

  8. Urabe H and Yang C C. On factorization of entire functions satisfying differential equations. Kodai Math J, 14: 123–133 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gundersen G. Finite order solutions of second order linear differential equations. Trans Amer Math Soc, 305: 415–429 (1988)

    Article  MathSciNet  Google Scholar 

  10. Gundersen G. Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates. J. London Math Soc, 37: 88–104 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  11. Chen Z X. On the growth of solutions of a class of higher order differential equations. Chin Ann of Math, 24B(4): 501–508 (2003)

    Article  Google Scholar 

  12. Chen Z X. The growth of solutions of f″ + e −z f′ + Q(z)f = 0 where the order (Q) = 1. Sci China Ser A, 45(3): 290–300 (2002)

    MATH  MathSciNet  Google Scholar 

  13. Chen Z X, Yang C C. Some further results on the zeros and growths of entire solutions of second order linear differential equations. Kodai Math J, 22: 273–285 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  14. Frank G, Hellerstein S. On the meromorphic solutions of non-homogeneous linear differetial equations with polynomial coefficients. Proc London Math Soc, 53(3): 407–428 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  15. Bank S, Laine I. Representations of solutions of periodic second order linear differential equations. J Reine Angew Math, 344: 1–21 (1983)

    MATH  MathSciNet  Google Scholar 

  16. He Y Z, Xiao X Z. Algebroid Functions and Ordinary Differential Equations (in Chinese). Beijing: Science Press, 1988

    Google Scholar 

  17. Ince E. Ordinary Differential Equations. New York: Dover Publications, 1927

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Zong-xuan Chen

  2. Department of Mathematics, College of Natural Sciences, Pusan National University, Pusan, 609-735, Karea

    Kwang Ho Shon

Authors
  1. Zong-xuan Chen
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  2. Kwang Ho Shon
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Corresponding author

Correspondence to Zong-xuan Chen.

Additional information

This work was supported by the Brain Pool Program of Korea Federation of Science and Technology Societies (No. 072-1-3-0164), NURI Academy of Banking, Derivatives and Securites and Insurance, and the Natural Science Foundation of Guangdong Province in China (Grant No. 06025059)

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Chen, Zx., Shon, K.H. On subnormal solutions of second order linear periodic differential equations. SCI CHINA SER A 50, 786–800 (2007). https://doi.org/10.1007/s11425-007-0050-3

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  • DOI: https://doi.org/10.1007/s11425-007-0050-3

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