Oscillation and nonoscillation criteria for even order nonlinear functional differential equations (Q2913829)

This paper is devoted to the study of the oscillatory and nonoscillatory behavior of even-order nonlinear functional differential equations with deviating argument of the type NEWLINE\[NEWLINE(p(t)| x^{(n)}(t)|^{\alpha}\operatorname{sgn}x^{(n)}(t))^{(n)}+q(t)| x(g(t))|^{\beta}\operatorname{sgn}x(g(t))=0,NEWLINE\]NEWLINE where the following conditions are assumed to hold: {\parindent=6mm\begin{itemize}\item[(a)] \(\alpha\) and \(\beta\) are positive constants, \item[(b)] \(p(t)\) and \(q(t)\) are positive continuous functions on \([a,\infty)\), \(a\geq 0\), \item[(c)] \(p(t)\) satisfies \(\int_a^{\infty}\frac{dt}{p(t)^{\frac{1}{\alpha}}}=\infty\), \item[(d)] \(g(t)\) is a positive continuously differentiable function on \([a,\infty)\) such that \(g'(t)>0\) and \(\lim_{t\to\infty}g(t)=\infty\).NEWLINENEWLINE\end{itemize}}