Interval criteria for oscillation of second-order impulsive delaydifferential equation with mixed nonlinearities
Authors :
V. Muthulakshmi* and R. Manjuram
Author Address :
Department of Mathematics, Periyar University, Salem-636 011, Tamilnadu, India.
*Corresponding author.
Abstract :
We obtain interval oscillation criteria for the second-order impulsive delay differential equation
\begin{gather*}
\big(r(t)\Phi_{\alpha}(x’(t))\big)’+p(t)\Phi_{\alpha}(x(t-\tau))
+\sum_{i=1}^n q_i(t)\Phi_{\beta_i}(x(t-\tau))=e(t),\, t\geq t_0, \, t\neq t_k,\\
x({t_k}^+)=a_k x({t_k}),\quad
x’({t_k}^+)=b_k x’({t_k}),\,\, k=1,2,3,...\,.
\end{gather*}
The results obtained in this paper extend some of the existing results. We have given some examples to illustrate our results.
Keywords :
Interval oscillation; Impulse; Delay; Mixed nonlinearities.
DOI :
Article Info :
Received : November 24, 2015; Accepted : May 15, 2016.
