On Meromorphic Solutions of a Certain Type of Nonlinear Differential Equations

Xiao Qing LU^{1}, Liang Wen LIAO^{2}, Jun WANG^{3}

1. Mathematics and Information Technology School, Jiangsu Second Normal University, Nanjing 210013, P. R. China; 2. Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China; 3. School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China

Abstract We consider transcendental meromorphic solutions with N(r, f)=S(r, f) of the following type of nonlinear differential equations:#br#f^{n}+P_{n-2}(f)=p_{1}(z)e^{α1(z)}+p_{2}(z)e^{α2(z)},#br#where n ≥ 2 is an integer, P_{n-2}(f) is a differential polynomial in f of degree not greater than n-2 with small functions of f as its coefficients, p_{1}(z), p_{2}(z) are nonzero small functions of f, and α_{1}(z), α_{2}(z) are nonconstant entire functions. In particular, we give out the conditions for ensuring the existence of meromorphic solutions and their possible forms of the above equation. Our results extend and improve some known results obtained most recently.

Xiao Qing LU,Liang Wen LIAO,Jun WANG. On Meromorphic Solutions of a Certain Type of Nonlinear Differential Equations[J]. Acta Mathematica Sinica, English Series, 2017, 33(12): 1597-1608.

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