机构地区: 贵州师范学院
出 处: 《华南师范大学学报(自然科学版)》 2014年第3期25-29,共5页
摘 要: 利用亚纯函数的Nevanlinna值分布理论的差分模拟,研究了非线性高阶差分方程P1(z)∏n i=1f(z+ci)=P2(z)f(z)n亚纯解的零点、极点收敛指数和增长级,其中n是一个正整数,ci(i=1,…,n)是非零复常数,P1(z)和P2(z)是非零多项式.在给定条件下,得到了这类差分方程亚纯解的增长级的精确估计. By utilizing the difference analogue of Nevanlinna's value distribution theory of meromorphic functions,the exponents of convergence of zeros,poles and the order of growth of meromorphic solutions of the nonlinear high order difference equation P1( z) ∏f( z + ci) =P2( z) f( z)^n are studied,where n is a positive integer,ci( i =1,…,n) are non-vanishing complex constants,and P1( z),P2( z) are given non-vanishing polynomials. The accurate estimate of the order of growth of meromorphic solutions to this difference equation is attained under the given conditions.