• Title/Summary/Keyword: Meromorphic

Search Result 241, Processing Time 0.02 seconds

ON TRANSCENDENTAL MEROMORPHIC SOLUTIONS OF CERTAIN TYPES OF DIFFERENTIAL EQUATIONS

  • Banerjee, Abhijit;Biswas, Tania;Maity, Sayantan
    • Bulletin of the Korean Mathematical Society
    • /
    • v.59 no.5
    • /
    • pp.1145-1166
    • /
    • 2022

  • In this paper, for a transcendental meromorphic function f and α ∈ ℂ, we have exhaustively studied the nature and form of solutions of a new type of non-linear differential equation of the following form which has never been investigated earlier: $$f^n+{\alpha}f^{n-2}f^{\prime}+P_d(z,f)={\sum\limits_{i=1}^{k}}{p_i(z)e^{{\alpha}_i(z)},$$ where Pd(z, f) is a differential polynomial of f, pi's and αi's are non-vanishing rational functions and non-constant polynomials, respectively. When α = 0, we have pointed out a major lacuna in a recent result of Xue [17] and rectifying the result, presented the corrected form of the same equation at a large extent. In addition, our main result is also an improvement of a recent result of Chen-Lian [2] by rectifying a gap in the proof of the theorem of the same paper. The case α ≠ 0 has also been manipulated to determine the form of the solutions. We also illustrate a handful number of examples for showing the accuracy of our results.

  • https://doi.org/10.4134/BKMS.b210637 인용 PDF KSCI