Interval oscillation of second-order Emden-Fowler neutral delay differential equations

Chen, Mu ; Xu, Zhiting

Electronic Journal of Differential Equations, Tome 2007 (2007).

Résumé

Summary: Employing Riccati techniques and the integral averaging method, we establish interval oscillation criteria for the second-order Emden-Fowler neutral delay differential equation $$ [|x'(t)|^{\gamma-1}x'(t)]'+q_1(t)|y(t-\sigma)|^{\alpha-1}y(t-\sigma) +q_2(t)|y(t-\sigma)|^{\beta-1} y(t-\sigma)=0, $$ where $t\geq t_0$ and $x(t)=y(t)+p(t)y(t-\tau)$. The criteria obtained here are different from most known criteria in the sense that they are based on information only on a sequence of subintervals of $[t_0,\infty)$, rather than on the whole half-line. In particular, two interesting examples that illustrate the importance of our results are included.

Détail

Classification : 34K40, 34K11, 34C10
Keywords: interval oscillation, neutral delay differential equation, Emden-Fowler, Riccati technique, integral averaging method