一类非线性微分方程的超越亚纯函数解
应用亚纯函数的Nevanlinna值分布理论，研究一类非线性微分方程

DOI: 10.12677/pm.2026.161026, PP. 238-246

方洋

Keywords: Nevanlinna理论，非线性微分方程，亚纯解
Nevanlinna Theory, Nonlinear Differential Equation, Meromorphic Solutions

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Abstract:

This study employed Nevanlinna theory to examine finite-order meromorphic solutions of nonlinear differential equations with the form $f^n+a{f}^{n？2}{f}^{″}+P_d\left(z,f\right)=p_1\left(z\right){\text{e}}^{a_1\left(z\right)}+p_2\left(z\right){\text{e}}^{a_2\left(z\right)}+p_3\left(z\right){\text{e}}^{a_3\left(z\right)}$ Where $P_d\left(z,f\right)$ is polynomial of degree $d$ , $p_i\left(i=1,2,3\right)$ are non-zero constants, and $a_i\left(z\right)\left(i=1,2,3\right)$ are distinct non-constant polynomials. Corresponding examples are provided for illustration.

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