본문 바로가기
KERD
논문KCI 등재

Growth order of Meromorphic Solutions of Higher-orderLinear Differential Equations

3

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

In this paper, we investigate higher-order linear differential equations with entire coefficients of iterated order. We improve and extend the result of L. Z. Yang by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen and the extended Wiman-Valiron theory by Wang and Yi. We also consider the nonhomogeneous linear differential equations.

Abstract

In this paper, we investigate higher-order linear differential equations with entire coefficients of iterated order. We improve and extend the result of L. Z. Yang by using the estimates for the logarithmic derivative of a transcendental meromorphic function due to Gundersen and the extended Wiman-Valiron theory by Wang and Yi. We also consider the nonhomogeneous linear differential equations.

참고문헌 (14)

  1. T. B. Cao, "On the iterated order of meromorphic solutions of higher order linear differential equations", Ann. of Diff. Eqs, 21, pp.111~122 (2005)
  2. Z. X. Chen, "The growth of solutions of differential equation f 00+e-zf0+Q(z)f = 0", Science in China (series A), 31, pp.775~784 (2001)
  3. Z. X. Chen, "The zero, pole and order of meromorphic solutions of differential equations with meromorphic coefficients", Kodai Math. J, 19, pp.341~354 (1996)
  4. Z. X. Chen, "Some further results on the zeros and growths of entire solutions of second order linear differential equations", Kodai Math. J, 22, pp.273~285 (1999)
  5. M. Frei, "¨ Uber die subnormalen L¨osungen der Differentialgleichungen w 00 + e−zw 0 + (konst.)f = 0", Comment Math. Helv, 36, pp.1~8 (1961)
  6. G. Gundersen, "Estimates for the logarithmic derivative of a meromorphic function, Plus Similar Estimates", J. London Math. Soc, 37, pp.88~104 (1988)
  7. G. Gundersen, "Finite order solutions of second order linear differential equations", Tran. Amer. Math. Soc, 305, pp.415~429 (1988)
  8. W. Hayman, "Meromorphic Functions" (1964), Clarendon Press, Oxford
  9. L. Kinnunen, "Linear differential equations with solutions of finite iterated order", Southeast Asian Bull. Math, 22, pp.385~405 (1998)
  10. I. Laine, "Nevanlinna theory and complex differential equations" (1993), Walter de Gruyter, Berlin-New York
  11. J. Wang, "Fixed points and hyper order of differential polynomials generated by solutions of differential equation", Complex Var. Theory Appl, 48, pp.83~94 (2003)
  12. L. Yang, "Value Distribution Theory and New Research" (1982), Beijing, Science press
  13. L. Z. Yang, "Growth of linear differential equations and their applications", Israel J. Math, 147, pp.359~372 (2005)
  14. H. X. Yi, "The Uniqueness Theory of Meromorphic Functions" (1995), Science Press, Beijing

관련 논문AI추천

이 간행물의 다른 논문 (14건)