Close-to-convex Function Generates Remarkable Solution of 2^nd order Complex Nonlinear Differential Equations

Abstract

    Consider the complex nonlinear differential equation  where  are complex coefficients, and  be a complex function performs non- homogeneous term of given equation.

In  this paper,  we investigated that    is a remarkable solution of given equation and belongs to hardy space  ; with studying the growth of  that solution  by two ways ; through the maximum modulus and Brennan’s Conjecture and  another  by finding the supremum  function of a volume of the surface area  . Furthermore,  we discussed the  solution behaviour  with meromorphic coefficients properties for given equation.