Global behavior of the solutions to a class of nonlinear, singular second order ODE

摘要

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, 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.