On Meromorphic Solutions of a Certain Type of Nonlinear Differential Equations  

作　　者：Xiao Qing LU Liang Wen LIAO Jun WANG 

机构地区：[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

出　　处：《Acta Mathematica Sinica,English Series》2017年第12期1597-1608,共12页数学学报（英文版）

基　　金：Sponsored by NNSF of China(Grant No.11671191);Natural Science Foundation of Shanghai(Grant No.17ZR1402900)

摘　　要：We consider transcendental merornorphic solutions with N（r, f） = S（r, f） of the following type of nonlinear differential equations：f^n ＋ Pn-2（f） = p1（z）e~α1（z） ＋ p2（z）^α2（z）,where n ≥2 is an integer, Pn-2（f） is a differential polynomial in f of degree not greater than n-2 with small functions of f as its coefficients, p1（z）, p2（z） are nonzero small functions of f1 and α1（z）, α2（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.We consider transcendental merornorphic solutions with N（r, f） = S（r, f） of the following type of nonlinear differential equations：f^n ＋ Pn-2（f） = p1（z）e~α1（z） ＋ p2（z）^α2（z）,where n ≥2 is an integer, Pn-2（f） is a differential polynomial in f of degree not greater than n-2 with small functions of f as its coefficients, p1（z）, p2（z） are nonzero small functions of f1 and α1（z）, α2（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.

关 键 词：Meromorphic solutions nonlinear differential equations small functions Nevanlinna＇s value distribution theory 

分 类 号：O175[理学—数学]