Oscillation of second order differential equations with mixed nonlinearities

Authors : Zhiting Xuq Aijun CHENG

Pages : 688-705

Doi:10.3906/mat-1209-49

View : 8 | Download : 8

Publication Date : 0000-00-00

Article Type : Research Paper

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*} insert ignore into journalissuearticles values(rinsert ignore into journalissuearticles values(t);|x\primeinsert ignore into journalissuearticles values(t);|a-1x\primeinsert ignore into journalissuearticles values(t););\prime+q0insert ignore into journalissuearticles values(t);|xinsert ignore into journalissuearticles values(t0insert ignore into journalissuearticles values(t););|a-1xinsert ignore into journalissuearticles values(t0insert ignore into journalissuearticles values(t);); +\sum\limitsi = 1nqiinsert ignore into journalissuearticles values(t);|xinsert ignore into journalissuearticles values(tiinsert ignore into journalissuearticles values(t););|ai-1xinsert ignore into journalissuearticles values(tiinsert ignore into journalissuearticles values(t);); = 0, \end{equation*} where a>0, ai>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.
Keywords : Oscillation, interval oscillation, mixed nonlinearities, delay differential equations