Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

ANGULAR DISTRIBUTION OF SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

  • Wu, Zhaojun (DEPARTMENT OF MATHEMATICS XIANNING UNIVERSITY) ;
  • Sun, Daochun (SCHOOL OF MATHEMATICS SOUTH CHINA NORMAL UNIVERSITY)
  • Published : 2007.11.30
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we study the location of zeros and Borel direction for the solutions of linear homogeneous differential equations $$f^{(n)}+A_{n-1}(z)f^{(n-1)}+{\cdots}+A_1(z)f#+A_0(z)f=0$$ with entire coefficients. Results are obtained concerning the rays near which the exponent of convergence of zeros of the solutions attains its Borel direction. This paper extends previous results due to S. J. Wu and other authors.

Keywords

References

  1. B. Belaidi, Estimation of the hyper-order of entire solutions of complex linear ordinary differential equations whose coeffcients are entire functions, Electron. J. Qual. Theory Differ. Equ. 2002 (2002), no. 5, 1-8
  2. C. T. Chuang, On Borel directions of meromorphic functions of infinite order. II, Bull.Hong Kong Math. Soc. 2 (1999), no. 2, 305-323
  3. H. Guo, J. H. Zheng, and T. W. Ng, On a new singular direction of meromorphic functions, Bull. Austral. Math. Soc. 69 (2004), no. 2, 277-287 https://doi.org/10.1017/S0004972700036017
  4. W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs Clarendon Press, Oxford 1964
  5. K. H. Kwon, On the growth of entire functions satisfying second order linear differential equations, Bull. Korean Math. Soc. 33 (1996), no. 3, 487-496
  6. I. Laine, Nevanlinna theory and complex differential equations, de Gruyter Studies in Mathematics, 15. Walter de Gruyter & Co., Berlin, 1993
  7. J. K. Langley, Some oscillation theorems for higher order linear differential equations with entire coeffcients of small growth, Results Math. 20 (1991), no. 1-2, 517-529 https://doi.org/10.1007/BF03323190
  8. R. Nevanlinna, A Uber die Eigenschaften meromorpher Funktionen in einem Winkelraum, Acta Soc. Sci. Fenn. 50 (1925), no. 12, 1-45
  9. S. J.Wu, Angular distribution in complex oscillation theory, Sci. China Ser. A 48 (2005), no. 1, 107-114 https://doi.org/10.1360/03YS0159
  10. S. J.W, 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. C. F. Yi, Angular distribution of solutions of a higher-order differential equation, Acta Math. Sinica (Chin. Ser.) 48 (2005), no. 1, 133-140
  12. L. Yang, Value distribution theory, Translated and revised from the 1982 Chinese origi- nal. Springer-Verlag, Berlin; Science Press, Beijing, 1993
  13. L. Yang and C. C. Yang, Angular distribution of values of f f', Sci. China Ser. A 37 (1994), no. 3, 284-294
  14. J. H. Zheng, On transcendental meromorphic functions with radially distributed values, Sci. China Ser. A 47 (2004), no. 3, 401-416 https://doi.org/10.1360/02ys0210

Cited by

  1. RADIAL OSCILLATION OF LINEAR DIFFERENTIAL EQUATION vol.49, pp.5, 2012, https://doi.org/10.4134/BKMS.2012.49.5.911