Global Solvability and Oscillation Criteria for a Class of Second Order Nonlinear Ordinary Differential Equations, Containing Some Important Classical Models.

The Riccati equation method is used to establish some global solvability criteria for a classes of Lane–Emdem–Fowler and Van der Pol type equations. Two oscillation theorems are proved. The results obtained are applied to the Emden–Fowler equation and to the Van der Pol type equation. [ABSTRACT FROM AUTHOR]