On meromorphic solutions of Fermat type delay-differential equations with two exponential terms
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909595517059072 |
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| author | Xiang, Xuxu Long, Jianren Xia, Mengting Qin, Zhigao |
| author_facet | Xiang, Xuxu Long, Jianren Xia, Mengting Qin, Zhigao |
| contents | The existence of the meromorphic solutions to Fermat type delay-differential equation
\begin{equation}
f^n(z)+a(f^{(l)}(z+c))^m=p_1(z)e^{a_1z^k}+p_2(z)e^{a_2z^k}, \nonumber
\end{equation}
is derived by using Nevanlinna theory under certain conditions, where $k\ge1$, $m,$ $n$ and $l$ are integers, $p_i$ are nonzero entire functions of order less than $k$, $c$, $a$ and $a_i$ are constants, $i=1,2$.
These results not only improve the previous results from Zhu et al. [J. Contemp. Math. Anal. 59(2024), 209-219], Qi et al. [Mediterr. J. Math. 21(2024), article no. 122], but also completely solve two conjectures posed by Gao et al. [Mediterr. J. Math. 20(2023), article no. 167].
Some examples are given to illustrate these results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On meromorphic solutions of Fermat type delay-differential equations with two exponential terms Xiang, Xuxu Long, Jianren Xia, Mengting Qin, Zhigao Complex Variables 30D35, 39B32 The existence of the meromorphic solutions to Fermat type delay-differential equation \begin{equation} f^n(z)+a(f^{(l)}(z+c))^m=p_1(z)e^{a_1z^k}+p_2(z)e^{a_2z^k}, \nonumber \end{equation} is derived by using Nevanlinna theory under certain conditions, where $k\ge1$, $m,$ $n$ and $l$ are integers, $p_i$ are nonzero entire functions of order less than $k$, $c$, $a$ and $a_i$ are constants, $i=1,2$. These results not only improve the previous results from Zhu et al. [J. Contemp. Math. Anal. 59(2024), 209-219], Qi et al. [Mediterr. J. Math. 21(2024), article no. 122], but also completely solve two conjectures posed by Gao et al. [Mediterr. J. Math. 20(2023), article no. 167]. Some examples are given to illustrate these results. |
| title | On meromorphic solutions of Fermat type delay-differential equations with two exponential terms |
| topic | Complex Variables 30D35, 39B32 |
| url | https://arxiv.org/abs/2504.15907 |