Global behavior of the Solutions to a Class of Nonlinear, Singular Second Order ODE

Abstract

In this paper the initial value problem and global properties of solutions are studied for the scalar second order ODE: $(|u^{\prime }{|}^l{u}^{\prime }{)}^{\prime }+c|u^{\prime }{|}^{\alpha }{u}^{\prime }+d|u{|}^{\beta }u=0$, where $\alpha ,\beta ,l,c,d$ are positive constants. In particular, existence, uniqueness and regularity as well as optimal decay rates of solutions to 0 are obtained depending on the various parameters, and the oscillatory or non-oscillatory behavior is elucidated.