Unbounded solutions for differential equations with mixed nonlinearities

What is it about?

We study unbounded solutions with different asymptotic behavior for a second order nonlinear differential equation. We also study the oscillation of all solutions and we show some discrepancies and similarities between equations of Emden-Fowler type and equations with mixed nonlinearities.

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Why is it important?

In asymptotic theory for second-order differential equations, an interesting question arises: can the three types of nonoscillatory solutions coexist? Our results extend to equation with mixed nonlinearities recent ones, in which a similar problem has been considered for the Emden-Fowler equation.