一类微差分方程整函数解的性质

The Properties of Entire Solutions of a Certain Type of Differential-Difference Equations

利用值分布理论对一类微差分方程f(z)~n+P(f)=β_1e^(α1^z)+β_2e^(α2^z)+β_3e^(α3^z)的整函数解的存在性、增长性和零点收敛指数进行了研究,其中α_i,β_i(i=1,2,3)为复常数,P(f)为f(z)的1阶微差分多项式,并推广了已有的一些结论.

By using the value distribution theory,the existence,growth and exponent of convergence of zeros of entire solutions of a certain type of differential-difference equations of the form f(z)^n+P(f)=β1e^α1z+β2^α2z+β3e^α3z are considered,whereαi,βi(i=1,2,3)are constants.P(f)denotes an algebraic differential-difference polynomial in f(z)of degree one.And some known results obtained most recently are improved.