On the Growth of Solutions of a Class of Higher Order Linear Differential Equations with Extremal Coefficients

We consider that the linear differential equations f(k)+Ak-1(z)f(k-1)+⋯+A1(z)f′+A0(z)f=0, where Aj (j=0,1,…,k-1), are entire functions. Assume that there exists l∈{1,2,…,k-1}, such that Al is extremal for Yang's inequality; then we will give some conditions on other coefficients which can guarantee that every solution f(≢0) of the equation is of infinite order. More specifically, we estimate the lower bound of hyperorder of f if every solution f(≢0) of the equation is of infinite order.