Growth and Bounded Solution of Second-Order of Complex Differential Equations Through of Coefficient Function

Abstract

The purpose of this research paper, is to present the second- order homogeneous complex differential equation f" + H(z)f = 0, which defined on the disk D = {z ∈ ℂ : |z − i| ≤ 1} ⊆ ℂ, where H(z) = e p(z), to show it an invariant by applying Liouville and self-adjoint transformation with an examine the convexity property of its coefficient H(z) = e p(z), in order to study the growing and bounded solution of consider equation.