Oscillation of second order neutral delay differential equations of Emden-Fowler type
The author presents some oscillation criteria for the second-order nonlinear neutral delay differential equation \[ [y(t)-py(t-\tau)]''+q(t)y^{\lambda}(g(t))\, {\text{sgn}}\, y(g(t))=0,\quad t\geq t_0, \] with \(q,g\in C([t_0,\infty), \mathbb{R}^+)\), \(\tau\geq 0\), \(g(t)\leq t\), \(g'(t)>0\), \(\lim_{t\to\infty}g(t)=\infty\), \(0\leq p<1\) and \(\lambda>0\). His results present some extended Kamenev and Philos-type theorems ensuring that every solution of this equation oscillates, and solve an open problem posed by \textit{James S. W. Wong} [J. Math. Anal. Appl. 252, 342--352 (2000; Zbl 0976.34057)] to find some oscillation criteria for this neutral differential equation.
second-order nonlinear neutral delay differential equations
scientific article; zbMATH DE number 2099108