Tomoyuki Tanigawa

Oscillation Criteria for a Class of Higher Order Nonlinear Differential Equations

abstract:
The higher order nonlinear differential equation
$$ \big(|x^{(n)}|^{\alpha}\sgn x^{(n)}\big)^{(n)}+q(t)|x|^{\beta}\sgn x= 0 $$
is considered, where $\alpha$ and $\beta$ are distinct positive constants and $q\!: \![0,+\infty)\!\to [0,+\infty)$ is a continuous function. Necessary and sufficient conditions for oscillation of all proper solutions of this equation are established.

Mathematics Subject Classification: 34C10, 34C15

Key words and phrases: Oscillation theory; Higher order nonlinear differential equations