Oscillation of second order differential equations with mixed nonlinearities

Authors

ZHITING XU
AIJUN CHENG

Abstract

By refining the standard integral averaging technique, in this paper, new oscillation criteria as well as interval oscillation criteria are established for the second order delay differential equation with mixed nonlinearities \begin{equation*} (r(t) x^{\prime}(t) ^{\alpha-1}x^{\prime}(t))^{\prime}+q_0(t) x(\tau_0(t)) ^{\alpha-1}x(\tau_0(t)) +\sum\limits_{i = 1}^nq_i(t) x(\tau_i(t)) ^{\alpha_i-1}x(\tau_i(t)) = 0, \end{equation*} where \alpha>0, \alpha_i>0, i = 1,2,\cdots,n. Our results generalize and improve the known results in the literature. Examples are also given to illustrate the importance of our results.

DOI

10.3906/mat-1209-49

Keywords

Oscillation, interval oscillation, mixed nonlinearities, delay differential equations

First Page

688

Last Page

705

Recommended Citation

XU, ZHITING and CHENG, AIJUN (2014) "Oscillation of second order differential equations with mixed nonlinearities," Turkish Journal of Mathematics: Vol. 38: No. 4, Article 8. https://doi.org/10.3906/mat-1209-49
Available at: https://journals.tubitak.gov.tr/math/vol38/iss4/8