Oscillatory properties of third-order quasilinear difference equations

B. Selvaraja and M. Rajub,*

Oscillatory properties of third-order quasilinear difference equations

Authors :

B. Selvaraj^a and M. Raju^b,*

Author Address :

^a,bDepartment of Science and Humanities, Nehru Institute of Engineering and Technology, Coimbatore, Tamil Nadu, India.

Abstract :

Some new oscillation criteria are obtained for the third-order quasilinear difference equation $\Delta^2\left(p_n \left(\Delta x_n\right)^\alpha\right)- q_n\left(\Delta x_n\right)^\alpha+r_nf(x_n)=0,$ $n=0,1,2,...,$ where $\alpha > 0$ is the ratio of odd positive integers. The method uses techniques based on Schwarz’s inequality. Example is inserted to illustrate the result.

Keywords :

Oscillation, third order, quasilinear, di.erence equation, Schwarz’s inequality.

DOI :

Article Info :

Received : May 09, 2013; Accepted : August 16, 2013.