论文标题
某些类型的非线性差异方程的确切解决方案的确切解决方案
The exact entire solutions of certain type of nonlinear difference equations
论文作者
论文摘要
在本文中，我们考虑了非线性差方程的整个解决方案$$ f^3+ q（z）Δf= p_1 e^{α_1z}+ p_2 e^{α_2z} $$，其中$ q $是polynomial，$ p_1，p_1，p_2，α_1，α_1，α_2$ ne_2 $ ne_2 $ ne_2结果表明，如果$ f $是上述方程式的$ρ_2（f）<1 $的整个解决方案，则$ f（z）= e_1e^{\ frac {α_1z} {3}} {3}}}}}+e_2e+e_2e^{\ frac {\ frac {\ frac {α_2z}} $ e_____________________________________________ $ ers $ ersants $ ers $ ers $ e $ e $ e $ e $ e $ e $ e $ e $ e $同时，我们对[18]中张等人提出的猜想给出了肯定的答案。
In this paper, we consider the entire solutions of nonlinear difference equation $$f^3+q(z)Δf=p_1 e^{α_1 z}+ p_2 e^{α_2 z} $$ where $q$ is a polynomial, and $p_1, p_2, α_1, α_2$ are nonzero constants with $α_1\neq α_2$. It is showed that if $f$ is a non-constant entire solution of $ρ_2(f)<1$ to the above equation, then $f(z)=e_1e^{\frac{α_1 z}{3}}+e_2e^{\frac{α_2 z}{3}}, $ where $e_1$ and $e_2$ are two constants. Meanwhile, we give an affirmative answer to the conjecture posed by Zhang et al in [18].
