Interval criteria for oscillation of second-order impulsive delay differential equation with mixed nonlinearities

V. Muthulakshmi; R. Manjuram

doi:10.26637/mjm403/008

Abstract

We obtain interval oscillation criteria for the second-order impulsive delay differential equation
$$
\begin{aligned}
\left(r(t) \Phi_\alpha\left(x^{\prime}(t)\right)\right)^{\prime}+p(t) \Phi_\alpha(x(t-\tau))+\sum_{i=1}^n q_i(t) \Phi_{\beta_i}(x(t-\tau))\\=e(t), t \geq t_0, t \neq t_k \\
x\left(t_k^{+}\right)=a_k x\left(t_k\right), \quad x^{\prime}\left(t_k^{+}\right)=b_k x^{\prime}\left(t_k\right), k=1,2,3, \ldots
\end{aligned}
$$
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

Mathematics Subject Classification:

34C10, 34K11

Authors Imprint References Funding Related Articles Downloads

V. Muthulakshmi Department of Mathematics, Periyar University, Salem-636 011, Tamilnadu, India.
R. Manjuram Department of Mathematics, Periyar University, Salem-636 011, Tamilnadu, India.

Pages: 404-420
Date Published: 01-07-2016
Vol. 4 No. 03 (2016): Malaya Journal of Matematik (MJM)

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The authors thank the anonymous referee for his/her helpful suggestions. This work was supported by UGC-Special Assistance Programme(No.F.510/7/DRS-1/2016(SAP-1)) and R. Manjuram was supported by University Grants Commission, New Delhi 110 002, India (Grant No. F1-17.1/2013-14/RGNF-2013-14-SC- TAM-38915/(SA-III/Website)).