Two perturbation results on the linear differential function f″ ＋ Π（z）A（z）f = 0 are obtained, where Π（z） and A（z） are periodic entire functions with period 2πi and σe（Π） 〈 σe（A）.
This article investigates the property of linearly dependence of solutions f（z） and f（z ＋ 2πi） for higher order linear differential equations with entire periodic coefficients.
In this paper, we investigate the existence and the form of subnormal solution for a class of second order periodic linear differential equations, estimate the growth properties of all solutions, and answer the question raised by Gundersen and Steinbart.
