摘要
In this article, the zeros of solutions of differential equation f^（k）（z）＋A（z）f（z） = 0, are studied, where k 2, A（z） = B（e^z）, B（ζ） = g1（1/ζ） ＋ g2（ζ）, g1 and g2 being entire functions with g2 transcendental and σ（g2） not equal to a positive integer or infinity. It is shown that any linearly independent solutions f1, f2, . . . , fk of Eq.（＊） satisfy λe（f1 . . . fk） ≥ σ（g2） under the condition that fj（z） and fj（z＋ 2πi） （j = 1, . . . , k） are linearly dependent.
In this article, the zeros of solutions of differential equation f^（k）（z）＋A（z）f（z） = 0, are studied, where k 2, A（z） = B（e^z）, B（ζ） = g1（1/ζ） ＋ g2（ζ）, g1 and g2 being entire functions with g2 transcendental and σ（g2） not equal to a positive integer or infinity. It is shown that any linearly independent solutions f1, f2, . . . , fk of Eq.（＊） satisfy λe（f1 . . . fk） ≥ σ（g2） under the condition that fj（z） and fj（z＋ 2πi） （j = 1, . . . , k） are linearly dependent.
基金
supported by the National Natural Foundation of China (10871076)
the Startup Foundation for Doctors of Jiangxi Normal University (2614)
