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

In this paper the initial value problem and global properties of solutions are studied for the scalar second order ODE: $(|u'|^{l}u')' + c|u'|^αu' + d|u|^βu=0$, where $α,β,l,c, d$ 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.

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