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On the growth of solutions to linear complex differential equations on annuli

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In this note, we consider the growth of solutions to second order and higher order linear complex differential equations on annuli instead of the complex plane. We establish several theorems that are analogues of the results in the complex plane.

Abstract

In this note, we consider the growth of solutions to second order and higher order linear complex differential equations on annuli instead of the complex plane. We establish several theorems that are analogues of the results in the complex plane.

참고문헌 (12)

  1. A. A. Goldberg, "Value distribution of meromorphic functions" (2008), American Mathematical Society
  2. V. P. Havin, "Linear and complex analysis. Problem book 3. Part II" (1994), Springer-Verlag
  3. W. K. Hayman, "Meromorphic Functions, Oxford Mathematical Monographs" (1964), Clarendon Press
  4. J. Heittokangas, "On complex dierential equations in the unit disc", Ann. Acad. Sci. Fenn. Math. Diss, (122), pp.54~ (2000)
  5. A. Ya. Khrystiyanyn, "the Nevanlinna theory for meromorphic functions on annuli. I", Mat. Stud, 23(1), pp.19~30 (2005)
  6. A. Ya. Khrystiyanyn, "On the Nevanlinna theory for meromorphic functions on annuli. II", Mat. Stud, 24(1), pp.57~68 (2005)
  7. A. Kondratyuk, "Fourier series methods in complex analysis", pp.9~111 (2006), Univ. Joensuu
  8. I. Laine, "Nevanlinna Theory and Complex Dierential Equations" (1993), Walter de Gruyter & Co.
  9. N.Wu, "Growth of solutions to linear complex dierential equations in an angular region", Electron. J. Dierential Equations, 2013(183), pp.8~ (2013)
  10. N.Wu, "On the growth order of solutions of linear dierential equations in a sector of the unit disk", Results Math, 65(1-2), pp.57~66 (2014)
  11. L. Yang, "Value Distribution Theory" (1993), Springer-Verlag
  12. J. Zheng, "Value Distribution of Meromorphic Functions" (2010), Tsinghua University Press

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