非线性复差分方程亚纯解的振荡性质

The Oscillating Property of the Meromorphic Solution of Nonlinear Difference Equations

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)+…+a_1(z)f(z+1)^(j_1)+a_0(z)f(z)^(j_0)=b(z),a_n(z)f(q^nz)^(j_n)+…+a_1(z)f(qz)^(j_1)+a_0(z)f(z)^(j_0)=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.

In this paper, we discuss the following difference equations an(z)f(z+n)jn+…+a1(z)f(z+1)j1+a0(z)f(z)j0 = b(z)an(z)f(qnz)jn+…+a1(z)f(qz)j1+a0(z)f(z)j0 =b(z),where ai(z)(i= 0,1,…, n) and b(z) are nonzero rational functions,ji(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.