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-1}f^{(k-1)}+...+A_{1}f'+A_{0}f=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.