Access the full text.
Sign up today, get DeepDyve free for 14 days.
In this paper, we study the existence of entire solutions of finite-order of non-linear difference equations of the form $$\begin{aligned} f^{n}(z)+q(z)\Delta _{c}f(z)=p_{1}\mathrm{e}^{\alpha _{1}z}+p_{2}\mathrm{e}^{\alpha _{2}z},\quad n\ge 2 \end{aligned}$$ f n ( z ) + q ( z ) Δ c f ( z ) = p 1 e α 1 z + p 2 e α 2 z , n ≥ 2 and $$\begin{aligned} f^{n}(z)+q(z)\mathrm{e}^{Q(z)}f(z+c)=p_{1}\mathrm{e}^{\lambda z}+p_{2}\mathrm{e}^{-\lambda z},\quad n\ge 3 \end{aligned}$$ f n ( z ) + q ( z ) e Q ( z ) f ( z + c ) = p 1 e λ z + p 2 e - λ z , n ≥ 3 where q, Q are non-zero polynomials, $$c,\lambda ,p_{i},\alpha _{i}(i=1,2)$$ c , λ , p i , α i ( i = 1 , 2 ) are non-zero constants such that $$\alpha _{1}\ne \alpha _{2}$$ α 1 ≠ α 2 and $$\Delta _{c}f(z)=f(z+c)-f(z)\not \equiv 0$$ Δ c f ( z ) = f ( z + c ) - f ( z ) ≢ 0 . Our results are improvements and complements of Wen et al. (Acta Math Sin 28:1295–1306, 2012), Yang and Laine (Proc Jpn Acad Ser A Math Sci 86:10–14, 2010) and Zinelâabidine (Mediterr J Math 14:1–16, 2017).
Computational Methods and Function Theory – Springer Journals
Published: Aug 27, 2018
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.