Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SOME RESULTS ON MEROMORPHIC SOLUTIONS OF CERTAIN NONLINEAR DIFFERENTIAL EQUATIONS

  • Li, Nan (School of Mathematics Qilu Normal University) ;
  • Yang, Lianzhong (School of Mathematics Shandong University)
  • Received : 2019.05.29
  • Accepted : 2019.10.16
  • Published : 2020.09.30
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Abstract

In this paper, we investigate the transcendental meromorphic solutions for the nonlinear differential equations $f^nf^{(k)}+Q_{d_*}(z,f)=R(z)e^{{\alpha}(z)}$ and fnf(k) + Qd(z, f) = p1(z)eα1(z) + p2(z)eα2(z), where $Q_{d_*}(z,f)$ and Qd(z, f) are differential polynomials in f with small functions as coefficients, of degree d* (≤ n - 1) and d (≤ n - 2) respectively, R, p1, p2 are non-vanishing small functions of f, and α, α1, α2 are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of these kinds of meromorphic solutions and their possible forms of the above equations.

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Acknowledgement

The authors would like to thank the referee for his/her thorough review with constructive suggestions and comments on the paper.

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