Growth of Solutions of a Class of Higher-Order Differential Equations with Coefficients Being Fabry Gap

This paper investigates the growth of solutions of a class of higher-order nonhomogeneous linear differential equation f^(k)+A_k-1f^(k-1)+...+A_1f'+A_0f=F and its homogeneous linear differential equation, where A_0,A_1,...A_k-1,F are entire functions and the dominant coefficient A_d has fabry gap, we obtain general estimates of the growth and zeros of entire transcendtial solutions of higher order linear differential equations.