Close-to-convex Function Generates Remarkable Solution of 2^nd order Complex Nonlinear Differential Equations
Journal of Al-Qadisiyah for Computer Science and Mathematics,
2017, Volume 9, Issue 2, Pages 141-147
AbstractConsider the complex nonlinear differential equation f^'' (z)-2/z f^' (z)-2/z^2 f^3 (z)= H(z) , where P(z)= (-2)/z,Q(z)=(-2)/z^2 are complex coefficients, and H(z) be a complex function performs non- homogeneous term of given equation.
In this paper, we investigated that w(z)=(zf^')/f is a remarkable solution of given equation and belongs to hardy space H^2 ; 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 〖K 〗_θ. Furthermore, we discussed the solution behaviour with meromorphic coefficients properties for given equation.
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