Oscillation criteria for nonlinear difference equations with superlinear neutral term

B. Kamaraj a,∗ and R. Vasuki b

Oscillation criteria for nonlinear difference equations with superlinear neutral term

Authors :

B. Kamaraj ^a,∗ and R. Vasuki ^b

Author Address :

^a,bDepartment of Mathematics, S.I.V.E.T College, Chennai-73, Tamil Nadu, India.

Abstract :

In this paper, the authors obtain sufficient conditions for the oscillation of all solutions of the equation
egin{equation*}
Delta(a_nDelta(x_n+p_nx_{n-k}^{alpha}))+q_nx_{n+1-l}^{eta}=0
end{equation*}
where $alphageq1$ and $eta>0$ are ratio of odd positive integers, and ${a_n}$, ${p_n}$ and ${q_n}$ are real positive sequences. Examples are provided to illustrate the importance of the main results.

Keywords :

Oscillation, nonlinear difference equation, superlinear neutral term.

DOI :

Article Info :

Received : April 07, 2017; Accepted : June 12, 2017.