Interaction between coefficient conditions and solution conditions of differential equations in the unit disk

where f #(z)= | f ′(z)|/(1 + | f (z)|2) is the spherical derivative of f . In Pommerenke [12] and more recent studies of Heittokangas [8], Benbourenane [3], and Chen and Shon [5], investigations have been made for linear differential equations in the unit disk D regarding the interplay between the behavior of the equation’s coefficients and that of its solutions. In this paper we consider in D the equation