Interval Oscillation Criteria for Super-Half-Linear Impulsive Differential Equations with Delay

Abstract

We study the following second-order super-half-linear impulsive differential equations with delay $[r(t){\phi }_{\gamma }(x\prime (t))]\prime +p(t){\phi }_{\gamma }(x(t-\sigma ))+q(t)f(x(t-\sigma ))=e(t)$, $t\ne {\tau }_k$, $x(t^{+})=a_{k}x(t),x\prime (t^{+})=b_{k}x\prime (t)$, $t={\tau }_k$, where $t\ge t_0\in ℝ$, ${\phi }_{*}(u)=|u{|}^{*-1}u$, $\sigma$ is a nonnegative constant, $\{{\tau }_k\}$ denotes the impulsive moments sequence with , ${\lim \hspace{0.17em}}_{k\to \infty }{\tau }_k=\infty$, and ${\tau }_{k+1}-{\tau }_k>\sigma$. By some classical inequalities, Riccati transformation, and two classes of functions, we give several interval oscillation criteria which generalize and improve some known results. Moreover, we also give two examples to illustrate the effectiveness and nonemptiness of our results.