Solutions of linear differential equations having maximal growth (Q1914826)

Consider the linear differential equation (1) \(w^{(n)} + \sum^n_{j = 1} A_j (z) \cdot w^{(n - j)} = 0\) where \(A_j (z)\) are entire functions. Each solution of (1) is also an entire function. If at least one of the coefficients \(A_j (z)\) of (1) is an entire transcendental function then equation (1) has always an integral solution of infinite order. A comparison function on basis of the coefficients of equation (1) is constructed as a measure of growth for solutions of (1).