一类高阶线性微分方程解的增长性

On the hyper-order of solutions of some higher order linear differential equations

研究一类高阶线性微分方程f^(κ)+H_κ-1f^(κ-1)+…+H_1f'+H_0f=0解的性质,其中H_j=A_(j1)(z)e^P_(j1)(z)+A_(j2)(z)e^p_(j2)(z)(j=0,1,…,k-1),P_(jq)(q=1,2)是n次复系数多项式,A_(jq)(z)是级小于n的整函数,当P_(jq)首项系数的主幅角不全相等时,得到这类方程的超越解有无穷级且超级为n。

This paper pays attention to investigate the solutions of f（k） ＋ Hk-1f（k-1） ＋ … ＋ Hlf＇ ＋ Hof = 0 where H3 = Ajl （z）ep^l（z） ＋ Aj2（z）ePj2（z）（j = O, 1,... , k - 1）, Pjq（q = 1, 2） are polynomials with complex coefficients and deg = n, Ajq（Z） are entire functions with a（Ajq） = n. When the argument of the first coefficient of Pjq is different, precise estimates of the growth of their transcendental solutions are obtained.