English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we mainly study the existence and the form of entire solutionswith finite order for the following system of Fermat-type difference andpartial differential-difference equations $$\begin{cases}f_1(z)^2+(\Delta_cf_2(z))^2=1\cr f_2(z)^2+(\Delta_cf_1(z))^2=1,\end{cases}$$$$\begin{cases} a_1^2f_1(z)^2+(a_2f_2(z+c)+a_3f_2(z))^2=1\cra_1^2f_2(z)^2+(a_2f_1(z+c)+a_3f_1(z))^2=1,\end{cases}$$ $$\begin{cases}(a_1f_1(z+c)+a_2f_1(z))^2+(a_3f_2(z+c)+a_4f_2(z))^2=1\cr(a_1f_2(z+c)+a_2f_2(z))^2+(a_3f_1(z+c)+a_4f_1(z))^2=1,\end{cases}$$ and$$\begin{cases}(\partial^{I}f_1(z)+\partial^{J}f_1(z))^{n_1}+f_2(z+c)^{m_1}=1\cr(\partial^{I}f_2(z)+\partial^{J}f_2(z))^{n_2}+f_1(z+c)^{m_2}=1\end{cases}$$ inseveral complex variables. Some of our results are improvements and extensionsof the previous theorems given by Zheng-Xu \cite{Zheng-Xu & Analysis math &2021}, Xu-Cao \cite{Xu & Cao & 2018}, Xu \textit{et. al.}\cite{Xu-Liu-Li-JMAA-2020} and Li \textit{et. al.} \cite{Li-Zhang-Xu & 2021 &AIMS}. Moreover, we give some examples which are relevant to the content of thepaper.

Entire solutions of system of Fermat-type difference and partial differential-difference equations in $ \mathbb{C}^2 $