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

Abstract

Employing Riccati techniques and the integral averaging method, we establish interval oscillation criteria for the second-order Emden-Fowler neutral delay differential equation $$ [|x'(t)|^{gamma-1}x'(t)]'+q_1(t)|y(t-sigma)|^{alpha-1}y(t-sigma) +q_2(t)|y(t-sigma)|^{eta-1} y(t-sigma)=0, $$ where $tgeq t_0$ and $x(t)=y(t)+p(t)y(t-au)$. 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.

Keywords

• Interval oscillation
• neutral delay differential equation
• Emden-Fowler
• Riccati technique
• integral averaging method.