Asymptotic behavior of solutions of a class of second order quasilinear ordinary differential equations (Q1612045)

Here, the second-order quasilinear ordinary differential equation \[ (|y'|^{\alpha-1}y')'= p(t)|y|^{\beta-1}y \] is considered. All solutions are classified into six classes according to their asymptotic behavior. Necessary and/or sufficient conditions are given on such equation to possess a solution of each of the six types.