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Asymptotic behavior of solutions of a class of second order quasilinear ordinary differential equations. (English) Zbl 1017.34053

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.

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
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