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http://dx.doi.org/10.4134/BKMS.b190744

EXPRESSIONS OF MEROMORPHIC SOLUTIONS OF A CERTAIN TYPE OF NONLINEAR COMPLEX DIFFERENTIAL EQUATIONS  

Chen, Jun-Fan (College of Mathematics and Informatics & Fujian Key Laboratory of Mathematical Analysis and Applications Fujian Normal University)
Lian, Gui (Ningbo Economic and Trade School)
Publication Information
Bulletin of the Korean Mathematical Society / v.57, no.4, 2020 , pp. 1061-1073 More about this Journal
Abstract
In this paper, the expressions of meromorphic solutions of the following nonlinear complex differential equation of the form $$f^n+Qd(z,f)=\sum\limits_{i=1}^{3}pi(z)e^{{\alpha}_i(z)}$$ are studied by using Nevanlinna theory, where n ≥ 5 is an integer, Qd(z, f) is a differential polynomial in f of degree d ≤ n - 4 with rational functions as its coefficients, p1(z), p2(z), p3(z) are non-vanishing rational functions, and α1(z), α2(z), α3(z) are nonconstant polynomials such that α'1(z), α'2(z), α'3(z) are distinct each other. Moreover, examples are given to illustrate the accuracy of the condition.
Keywords
Nonlinear differential equations; meromorphic solutions; Nevanlinna theory; zeros; order;
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