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http://dx.doi.org/10.4134/BKMS.b200265

THREE RESULTS ON TRANSCENDENTAL MEROMORPHIC SOLUTIONS OF CERTAIN NONLINEAR DIFFERENTIAL EQUATIONS  

Li, Nan (School of Mathematics Qilu Normal University)
Yang, Lianzhong (School of Mathematics Shandong University)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.4, 2021 , pp. 795-814 More about this Journal
Abstract
In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: fn + P(f) = R(z)eα(z) and fn + P*(f) = p1(z)eα1(z) + p2(z)eα2(z) in the complex plane, where P(f) and P*(f) are differential polynomials in f of degree n - 1 with coefficients being small functions and rational functions respectively, R is a non-vanishing small function of f, α is a nonconstant entire function, p1, p2 are non-vanishing rational functions, and α1, α2 are nonconstant polynomials. Particularly, we consider the solutions of the second equation when p1, p2 are nonzero constants, and deg α1 = deg α2 = 1. Our results are improvements and complements of Liao ([9]), and Rong-Xu ([11]), etc., which partially answer a question proposed by Li ([7]).
Keywords
Meromorphic functions; nonlinear differential equations; small functions; differential polynomials;
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