Skip to main content
SpringerLink
Log in

m Components-admissible solutions of systems of higher-order partial differential equations on C n

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

Using value distribution theory and techniques in several complex variables,we investigate the problem of existence of m components-admissible solutions of a class of systems of higher-order partial differential equations in several complex variables and estimate the number of admissible components of solutions. Some related results will also be obtained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Biancofiore, A., Stoll, W. A nother proof of the the lemma of the logarithmic derivative in several complex variables. in “Recent Developments in Several Complex Variables”, pp.29–45, Annals of Math. Studies, Vol.100, Princeton Univ. Press, Princeton, 1981

    Google Scholar 

  2. Gao, L.Y. On m admissible components of solutions. Complex Variables, 35(4): 297–306 (1998)

    MathSciNet  Google Scholar 

  3. Gao, L.Y. On admissible solution of two types of systems of complex differential equations. Acta Math. Sinica, 43(1): 149–156 (2000)

    MATH  MathSciNet  Google Scholar 

  4. Gao, L.Y. On the growth of components of meromorphic solutions of systems of complex differential equations. Acta Mathematicae Applicatae Sinica (English Series), 21(3): 499–504 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Gao, L.Y. Admissible meromorphic solutions of a system of complex algebraic differential equations. Novi Sad J.of Math., 29(1): 61–67 (1999)

    Google Scholar 

  6. Gao, L.Y., Sun, D.C., Xiao, X.Z. m-entire admissible solutions of a type of a system of algebraic differential equations. Kyungpook Math. J., 38(2): 341–350 (1998)

    MATH  MathSciNet  Google Scholar 

  7. He, Y.Z., Laine, I. The Hayman-Miles Theorem and the the differential equation (y′)n = R(z, y). Analysis, 10: 387–396 (1990)

    MATH  MathSciNet  Google Scholar 

  8. Hu, P.C., Yang, C.C. Further results on factorization of meromorphic solutions of partial differential equations. Results in Math., 30: 310–320(1996)

    MATH  MathSciNet  Google Scholar 

  9. Hu, P.C., Yang, C.C. Malmquist type theorem and factorization of meromorphic solutions of partial differential equations. Complex Variables, 27: 269–285 (1995)

    MATH  MathSciNet  Google Scholar 

  10. Li, Kamshun, Chan, Waileung. Meromorphic solutions of higher order systems of algebraic differential equations. Math.Scand., 71(1): 105–121 (1992)

    MATH  MathSciNet  Google Scholar 

  11. Mokhon’ko, A.Z., Mokhon’ko, V.D. Estimates for the Nevanlinna characteristic of some classes of meromorphic functions and their applications to differential equations. Sib.Math.J., 15: 921–934 (1974)

    Article  Google Scholar 

  12. Song, S.G. Meromorphic solutions of differential equations in the complex domain. Acta.Math.Sinica, 34: 779–784 (1991)

    MATH  MathSciNet  Google Scholar 

  13. Stoll, W. Value distribution theory in several complex variables. Shandong Seience and Technology Press, Jinan, 1995

    Google Scholar 

  14. Tu, Z.H. On meromorphic solutions of some algebraic differential equations on C n. J.of Math.Anal. and Appl., 214: 1–10 (1997)

    Article  MATH  Google Scholar 

  15. Tu, Z.H. Some Malmquist type theorems of partial differential equations on C n. J.of Math.Anal. and Appl., 179: 41–60 (1993)

    Article  MATH  Google Scholar 

  16. Vitter, A. The lemma of the logarithmic dervative in several complex variables. Duke Math. J., 44: 89–104 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  17. Ye, Z. On Nevanlinnas second main theorem in projective space. Invent. Math., 122: 475–507 (1995)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Jinan University, Guangzhou, 510632, China

    Ling-yun Gao

Authors
  1. Ling-yun Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ling-yun Gao.

Additional information

Supported by the National Natural Science Foundation of China (No. 10471065) and the Natural Science Foundation of Guangdong Province (No.04010474)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, Ly. m Components-admissible solutions of systems of higher-order partial differential equations on C n . Acta Math. Appl. Sin. Engl. Ser. 24, 211–220 (2008). https://doi.org/10.1007/s10255-005-5110-2

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-005-5110-2

Keywords

2000 MR Subject Classification

Search

Navigation