摘要：The main purpose of this paper is to give the Malmquist type result of the meromorphic solutions of a system of complex difference equations of the following form: { ∑ λ 1 ∈ I 1 , μ 1 ∈ J 1 α λ 1 , μ 1 ( z ) ( ∏ ν = 1 n f ( z + c ν ) l λ 1 , ν ∏ ν = 1 n g ( z + c ν ) m μ 1 , ν ) = ∑ i = 0 p a i ( z ) g ( z ) i ∑ j = 0 q b j ( z ) g ( z ) j , ∑ λ 2 ∈ I 2 , μ 2 ∈ J 2 β λ 2 , μ 2 ( z ) ( ∏ ν = 1 n f ( z + c ν ) l λ 2 , ν ∏ ν = 1 n g ( z + c ν ) m μ 2 , ν ) = ∑ k = 0 s d k ( z ) f ( z ) k ∑ l = 0 t e l ( z ) f ( z ) l , $$\left \{ \textstyle\begin{array}{l} \sum_{\lambda_) \in I_), \mu_)\in J_)}\alpha_{\lambda_), \mu_)}(z) (\prod_{\nu=1}^{n}f(z+c_{\nu})^{l_{\lambda_), \nu}}\prod_{\nu=1}^{n}g(z+c_{\nu})^{m_{\mu_), \nu}} ) = \frac{\sum_{i=0}^{p}a_{i}(z)g(z)^{i} }{\sum_{j=0}^{q}b_{j}(z)g(z)^{j}}, \\ \sum_{\lambda_, \in I_,, \mu_,\in J_,}\beta_{\lambda_,, \mu_,}(z) (\prod_{\nu =1}^{n}f(z+c_{\nu})^{l_{\lambda_,, \nu}}\prod_{\nu=1}^{n}g(z+c_{\nu})^{m_{\mu_,, \nu}} ) = \frac{\sum_{k=0}^{s}d_{k}(z)f(z)^{k} }{\sum_{l=0}^{t}e_{l}(z)f(z)^{l}}, \end{array} \right . $$ where c 1 , c 2 , … , c n $c_), c_,, \ldots, c_{n}$ are distinct, nonzero complex numbers, the coefficients α λ 1 , μ 1 ( z ) $\alpha_{\lambda_), \mu_)}(z)$ ( λ 1 ∈ I 1 $\lambda _) \in I_)$ , μ 1 ∈ J 1 $\mu_)\in J_)$ ), β λ 2 , μ 2 ( z ) $\beta_{\lambda_,, \mu_,}(z)$ ( λ 2 ∈ I 2 $\lambda_, \in I_,$ , μ 2 ∈ J 2 $\mu_,\in J_,$ ), a i ( z ) $a_{i}(z)$ ( i = 0 , 1 , … , p $i=0,1,\ldots, p$ ), b j ( z ) $b_{j}(z)$ ( j = 0 , 1 , … , q $j=0,1,\ldots, q$ ), d k ( z ) $d_{k}(z)$ ( k = 0 , 1 , … , s $k=0,1,\ldots, s$ ), and e l ( z ) $e_{l}(z)$ ( l = 0 , 1 , … , t $l=0,1,\ldots, t$ ) are small functions relative to f ( z ) $f(z)$ and g ( z ) $g(z)$ , I i = { λ i = ( l λ i , 1 , l λ i , 2 , … , l λ i , n ) l λ i , ν ∈ N ∪ { 0 } , ν = 1 , 2 , … , n } $I_{i} = \{\lambda _{i}=(l_{\lambda_{i}, 1}, l_{\lambda_{i}, 2}, \ldots, l_{\lambda_{i},n}) l_{\lambda_{i}, \nu}\in{N} \cup\{0\},\nu= 1,2,\ldots,n\}$ ( i = 1 , 2 $i=1,2$ ) and J j = { μ j = ( m μ j , 1 , m μ j , 2 , … , m μ j , n ) m μ j , ν ∈ N ∪ { 0 } , ν = 1 , 2 , … , n } $J_{j} = \{\mu_{j}=(m_{\mu_{j}, 1}, m_{\mu_{j}, 2}, \ldots, m_{\mu_{j},n}) m_{\mu_{j}, \nu}\in{N} \cup\{0\},\nu=1,2, \ldots,n\}$ ( j = 1 , 2 $j=1, 2$ ) are finite index sets. The growth of meromorphic solutions of a related system of complex functional equations is also investigated.
关键词：systems of complex difference equations ; meromorphic functions ; Malmquist type theorem ; functional equation
