Asymptotic analysis of Emden-Fowler type equation with an application to power flow models

Abstract

Emden-Fowler type equations are nonlinear differential equations that appear in many fields such as mathematical physics, astrophysics and chemistry. In this paper, we perform an asymptotic analysis of a specific Emden-Fowler type equation that emerges in a queuing theory context as an approximation of voltages under a well-known power flow model. Thus, we place Emden-Fowler type equations in the context of electrical engineering. We derive properties of the continuous solution of this specific Emden-Fowler type equation and study the asymptotic behavior of its discrete analog. We conclude that the discrete analog has the same asymptotic behavior as the classical continuous Emden-Fowler type equation that we consider.