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On meromorphic solutions of Fermat type delay-differential equations with two exponential terms (2504.15907v3)
Published 22 Apr 2025 in math.CV
Abstract: The existence of the meromorphic solutions to Fermat type delay-differential equation \begin{equation} fn(z)+a(f{(l)}(z+c))m=p_1(z)e{a_1zk}+p_2(z)e{a_2zk}, \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.