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THE ZEROS DISTRIBUTION OF SOLUTIONS OF HIGHER ORDER DIFFERENTIAL EQUATIONS IN AN ANGULAR DOMAIN

  • Huang, Zhibo ;
  • Chen, Zongxuan
  • Received : 2008.02.05
  • Published : 2010.05.31

Abstract

In this paper, we investigate the zeros distribution and Borel direction for the solutions of linear homogeneous differential equation $f^{(n)}+A_{n-2}(z)f^{(n-2)}+{\cdots}+A_1(z)f'+A_0(z)f=0(n{\geq}2)$ in an angular domain. Especially, we establish a relation between a cluster ray of zeros and Borel direction.

Keywords

zeros distribution;linear differential equation;hyper order;Borel direction

References

  1. Z. X. Chen and C. C. Yang, On the zeros and hyper-order of meromorphic solutions of linear differential equations, Ann. Acad. Sci. Fenn. Math. 24 (1999), no. 1, 215–224.
  2. Z. X. Chen and K. H. Shon, On the growth of solutions of a class of higher order differential equations, Acta Math. Sci. Ser. B Engl. Ed. 24 (2004), no. 1, 52–60.
  3. A. A. Gol’dberg and I. V. Ostrovskii, The Distribution of Values of Meromorphic Functions, Izdat. Nauka, Moscow, 1970.
  4. S. A. Gao, Z. X. Chen, and T. W. Chen, Oscillation theory of linear differential equation, Huazhong University of Science and Technology Press, 1998.
  5. W. K. Hayman, Meromorphic Function, Oxford, 1964.
  6. Y. Z. He and X. Z. Xiao, Algebroid functions and ordinary differential equations, Science Press, Beijing, 1998.
  7. Z. B. Huang and Z. X. Chen, Angular distribution with hyper-order in complex oscillation theory, (Chinese) Acta Math. Sinica (Chin. Ser.) 50 (2007), no. 3, 601–614.
  8. I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter & Co., Berlin, 1993.
  9. R. Nevanlinna, Uber die Eigenschaften meromorpher funktionen in einem winkelraum, Acta Soc. Sci. Fenn. 50 (1925), 1-45.
  10. S. J. Wu, On the location of zeros of solutions of f" + A(z)f = 0 where A(z) is entire, Math. Scand. 74 (1994), no. 2, 293–312.
  11. S. J. Wu, Angular distribution in complex oscillation theory, Sci. China Ser. A 48 (2005), no. 1, 107–114.
  12. Z. J. Wu and D. C. Sun, Angular distribution in complex oscillation, Acta Math. Sinica (Chin. Ser.) 50 (2007), no. 6, 1297–1304.
  13. L. Yang, Value Distribution Theory and its New Researches, Beijing Science Press, 1992.
  14. C. F. Yi, Angular distribution of solutions of a higher-order differential equation, Acta Math. Sinica (Chin. Ser.) 48 (2005), no. 1, 133-140.

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