The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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PROPERTIES OF SOLUTIONS OF LINEAR DIFFERENTIAL EQUATIONS IN THE COMPLEX PLANE

  • Chen, Zong-Xuan (SCHOOL OF MATHEMATICAL SCIENCES, SOUTH CHINA NORMAL UNIVERSITY) ;
  • Shon, Kwang-Ho (DEPARTMENT OF MATHEMATICS, COLLEGE OF NATURAL SCIENCES, PUSAN NATIONAL UNIVERSITY)
  • Received : 2010.03.11
  • Accepted : 2010.08.19
  • Published : 2010.08.31
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Abstract

We research the properties of solutions of general higher order homogeneous linear differential equations and apply the hyper order to obtain more precise estimation for the growth of solutions of infinite order.

Keywords

References

  1. Z. X. Chen and K. H. Shon : Hyper order of solutions of complex differential equations in the disc. J. Korea Soc. Math. Educ. 16 (2009), 155-165.
  2. I. Chyzhykov, G. Gundersen & J. Heittokangas : Linear differential equations and logarithmic derivative estimates. Proc. London Math. Soc. 86 (2003), 735-754. https://doi.org/10.1112/S0024611502013965
  3. W. Hayman : Meromorphic functions. Clarendon Press, Oxford, 1964.
  4. J. Heittokangas : On complex differential equations in the unit disc. Ann. Acad. Sci. Fenn. Math. Diss. 122 (2000), 1-54.
  5. CH. Pommerenke : On the mean growth of the solutions of complex linear differential equations in the disk. Complex Variables 1 (1982), 23-38. https://doi.org/10.1080/17476938208814004
  6. L. Yang : Value distribution theory, revised edition of the original Chinese edition. Springer-Verlag, Berlin, Science Press, Beijing, 1993.