Skip to main content
SpringerLink
Log in

Meromorphic solution of a class of non-linear differential equations with sharing one value

  • Original Research Paper
  • Published:
The Journal of Analysis Aims and scope Submit manuscript

Abstract

Here we report the finding of the meromorphic solution of a general differential equation which is in the form \(G^{(i)}=\sum _{k=0}^{j}c_{k}G^{k},\) where \(c_{0}, c_{1}, \ldots ,c_{j} \not \equiv 0 \) are small functions of G. The results concerning Linear, Riccati, Abel, Bernoulli, Ginzburg–Landau and Jacobi elliptic differential equations are obtained as special ones of the present study. Differential equations with transcendental nonlinearity are shown to be also covered by the present general study.

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. Al-Khaladi, A.H.H. 2005. On meromorphic functions that share one value with their derivative. Analysis 25: 131–140.

    Article  MathSciNet  Google Scholar 

  2. Al-Khaladi, A.H.H. 2011. Meromorphic functions that share one small function with their k-th derivative. Analysis 31: 341–354.

    Article  MathSciNet  Google Scholar 

  3. Al-Khaladi, A.H.H. 2013. Meromorphic functions that share one value and the solution of Riccati differential equation. Arab Journal of Mathematical Sciences 2: 129–137.

    Article  MathSciNet  Google Scholar 

  4. Cherry, W., and Z. Ye. 2001. Theory of Value Distribution. Springer Monographs in Mathematics. Berlin: Springer.

    Google Scholar 

  5. Cao, T.B., J.F. Xu, and Z.X. Chen. 2010. On the meromorphic solutions of linear differential equations on the complex plane. Journal of Mathematical Analysis and Applications 364: 130–142.

    Article  MathSciNet  Google Scholar 

  6. Fang, M.L. 2002. Uniqueness and value-sharing of entire functions. Computers and Mathematics with Applications 44: 828–831.

    MathSciNet  Google Scholar 

  7. Gundersen, G.G. 1983. Meromorphic functions that share two finite values with their derivative. Pacific Journal of Mathematics 105: 299–309.

    Article  MathSciNet  Google Scholar 

  8. Gundersen, G.G., and L.Z. Yang. 1998. Entire functions that share one value with one or two of their derivatives. Journal of Mathematical Analysis and Applications 223: 88–95.

    Article  MathSciNet  Google Scholar 

  9. Hayman, W.K. 1964. Meromorphic Functions. Oxford: Clarendon Press.

    MATH  Google Scholar 

  10. Laine, I. 1993. Nevanlinna Theory and Complex Differential Equations. Berlin: Walter de Gruyter.

    Book  Google Scholar 

  11. Li, P. 2008. Entire solutions of certain type of differential equations. Journal of Mathematical Analysis and Applications 344: 253–259.

    Article  MathSciNet  Google Scholar 

  12. Lin, X.Q., and W.C. Lin. 2011. Uniqueness of entire functions sharing one value. Journal of Mathematical Analysis and Applications 31B (3): 1062–1076.

    MathSciNet  MATH  Google Scholar 

  13. Tang, J.F., and L.W. Liao. 2007. The transcendental meromorphic solutions of a certain type of nonlinear differential equations. Journal of Mathematical Analysis and Applications 334: 517–527.

    Article  MathSciNet  Google Scholar 

  14. Whittaker, E.T., and Watson, G.N. 1927. A Course of Modern Analysis, Fourth Edition, Cambridge: Cambridge University Press (reissued 1996).

  15. Yang, C.C., and H.X. Yi. 2004. Uniqueness Theory of Meromorphic Functions. Dordrecht: Kluwer.

    Google Scholar 

  16. Zhang, X.Y., J.F. Chen, and W.C. Lin. 2008. Entire or meromorphic functions sharing one value. Computers and Mathematics with Applications 56: 1876–1883.

    Article  MathSciNet  Google Scholar 

  17. Siddheshwar P.G., and A. Tanuja. 2019. Existence of meromorphic solution of Riccati-Abel differential equation. In Rushi Kumar B., Sivaraj R., Prasad B., Nalliah M., and Reddy A. (eds) Applied Mathematics and Scientific Computing. Trends in Mathematics. Birkhäuser, Cham

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore, 560 056, India

    P. G. Siddheshwar

  2. Department of Mathematics, Siddaganga Institute of Technology, Tumkur, 572 103, India

    Tanuja Adaviswamy

  3. Department of Mathematics, Karnatak University, Dharwad, 580003, India

    Subhas S. Bhoosnurmath & Mahesh Barki

Authors
  1. P. G. Siddheshwar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tanuja Adaviswamy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Subhas S. Bhoosnurmath
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mahesh Barki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tanuja Adaviswamy.

Ethics declarations

Conflict of interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Human/animals participants

The authors declare that there is no research involving human participants and/or animals in the contained of this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Siddheshwar, P.G., Adaviswamy, T., Bhoosnurmath, S.S. et al. Meromorphic solution of a class of non-linear differential equations with sharing one value. J Anal 28, 415–430 (2020). https://doi.org/10.1007/s41478-019-00176-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41478-019-00176-2

Keywords

Mathematics Subject Classification

Search

Navigation