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′|lu′)′+c|u′|αu′+d|u|βu=0(|u′|lu′)′+c|u′|αu′+d|u|βu=0, where α,β,l,c,dα,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.