论文标题
某些非线性微分方程的先验杂晶溶液的三个结果
Three results on transcendental meromorphic solutions of certain nonlinear differential equations
论文作者
论文摘要
在本文中，我们研究了非线性微分方程的先验性杂形解决方案：$ f^{n}+p（f）= r（z）e^{α（z）} $和$ f^{n}+p _ {*}（f）= p_ {1}（z）e^{α_{1}（z）}+p_ {2}（z） $ n-1 $分别具有小函数和有理功能，$ r $是$ f $的不变小函数，$α$，$α$是一个非稳定的整个功能，$ p_ {1}，p_ {2} $是非呈现的，是非呈现的，是非呈现的，$α__{1}，<1}，α___ pony是poloton。特别是，当$ p_ {1}，p_ {2} $是非零常数，而$°α_{1} =°α_{2} = 1 $时，我们会考虑第二个方程的解决方案。我们的结果是LIAO的改进和补充（Complexvar。Elliptic等等，2015，60（6）：748--756）和RONG-XU（Mathematics 2019，7，539）等，部分回答了Li提出的问题（J. Math。Anal。Anl。Appl。2011，375：375：375：311，375：310：311，310---319）。
In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: $f^{n}+P(f)=R(z)e^{α(z)}$ and $f^{n}+P_{*}(f)=p_{1}(z)e^{α_{1}(z)}+p_{2}(z)e^{α_{2}(z)}$ 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, $p_{1}, p_{2}$ are non-vanishing rational functions, and $α_{1}, α_{2}$ are nonconstant polynomials. Particularly, we consider the solutions of the second equation when $p_{1}, p_{2}$ are nonzero constants, and $°α_{1}=°α_{2}=1$. Our results are improvements and complements of Liao (Complex Var. Elliptic Equ. 2015, 60(6): 748--756), and Rong-Xu (Mathematics 2019, 7, 539), etc., which partially answer a question proposed by Li (J. Math. Anal. Appl. 2011, 375: 310--319).
