【摘要】 该文主要研究以下两类非线性复差分方程a_n（z）f（z+n）^j_n+…+a₁（z）f（z+1）^j₁+a₀（z）f（z）^j₀=b（z）,a_n（z）f（qⁿz）^j_n+…+a₁（z）f（qz）^j₁+a₀（z）f（z）^j₀=b（z）,其中,a_i（z）（i=0,1,…,n）与b（z）为非零有理函数,j_i（i=0,1,…,n）为正整数,q为非零复常数.当上述方程的亚纯解的超级小于1并且极点较少时,对解的零点分布进行了估计.此外,当亚纯解具有无穷多个极点时,也对极点收敛指数给出下界.更多还原

【Abstract】 In this paper, we discuss the following difference equations a_n（z）f（z+n）^j_n+…+a₁（z）f（z+1）^j₁+a₀（z）f（z）^j₀ = b（z）a_n（z）f（qⁿz）^j_n+…+a₁（z）f（qz）^j₁+a₀（z）f（z）^j₀ =b（z）,where a_i（z）（i= 0,1,…, n） and b（z） are nonzero rational functions,j_i（i = 0,1,…, n） are positive integers, q is a nonzero complex constant. When the equations above have meromorphic solutions with hyper order less than 1 and few poles, we investigate the distributions of zeros.Besides, when the solution has infinitely many poles, we give the lower bound of the exponent of convergence of poles.更多还原