DOI QR코드

DOI QR Code

ESTIMATIONS FOR THE ORDER OF SOLUTIONS OF LINEAR COMPLEX DIFFERENTIAL EQUATIONS

  • 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 : 2012.05.02
  • Accepted : 2012.08.06
  • Published : 2012.08.31

Abstract

We research the properties of solutions of general higher order non-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 & K.H. Shon: On the growth of solutions of a class of higher order differential equations. Acta Math. Scientia Ser. B 24B (2004), 52-60.
  2. Z.X. Chen & K.H. Shon: The growth of solutions of differential equations with coeffcients of small growth in the disc. J. Math. Anal. Appl. 297 (2004), 285-304. https://doi.org/10.1016/j.jmaa.2004.05.007
  3. Z.X. Chen & K.H. Shon: On the growth and fixed points of solutions of second order differential equations with meromorphic coeffcients. Acta Math. Sinica, English Ser. 21 (2005), 753-764. https://doi.org/10.1007/s10114-004-0434-z
  4. Z.X. Chen & K.H. Shon: Hyper order of solutions of complex differential equations in the disc. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 16 (2009), 155-165.
  5. Z.X. Chen & K.H. Shon: The hyper order of solutions of second order differential equations and subnormal solutions of periodic equations. Taiwanese J. Math. 14 (2011), 611-628.
  6. M. Frei: Uber die losungen linearer differentialgleichungen mit ganzen funktionen als koeffzienten. Comment. Math. Helv. 35 (1961), 201-222. https://doi.org/10.1007/BF02567016
  7. W. Hayman: Meromorphic functions. Clarendon Press, Oxford, 1964.
  8. J. Heittokangas: On complex differential equations in the unit disc. Ann. Acad. Sci. Fenn. Math. Diss. 122 (2000), 1-54.
  9. 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
  10. H. Wittich: Zur Theorie linearer differentialgleichungen im komplexen. Ann. Acad. Sci. Fenn. Ser. A. I. 379 (1996), 1-18.
  11. L. Yang: Value distribution theory. Revised edition of the original Chinese edition. Springer-Verlag, Berlin, Science Press, Beijing, 1993.