ON ASYMPTOTIC BEHAVIOR OF POSITIVE SOLUTIONS OF  WITH  AND

Ichiro Tsukamoto (Japan)

Received March 9, 2009

Abstract

We consider the Emden-Fowler type differential equation of the form denoted in the title. This is carried out under initial conditions      and      Asymptotic behavior of the positive solution is shown for arbitrarily fixed T, A and every B in the first initial condition, and for arbitrarily fixed a and every b in the second initial condition. Actually this is achieved from getting analytical expressions of the solution valid in the neighborhoods of both ends of its domain.

Keywords and phrases: a second order nonlinear differential equation, asymptotic behavior, the first order rational differential equation, a two dimensional autonomous system, a Briot-Bouquet differential equation.