The main purpose of this article is to study the oscillatory behavior of solutions of the fourth-order DDE with damping, ∆ 4 u(n) + p(n)∆u(n + 1) + q(n)u(σ (n)) = 0 under the assumption that the auxiliary third order difference equation, ∆ 3 z(n) + p(n)z(n + 1) = 0 is nonoscillatory. In contrast with the existing results, the paper present oscillation of all solutions and simplify the examination process of oscillation. An example is provided to dwell upon the importance of the main result.
The author presents some sufficient conditions for second order difference equation
with damping term of the form
^(an ^(xn + cxn-k)) + pn^xn + qnf(xn+1-l) = 0
An example is given to illustrate the main results.
2010 AMS Subject Classification: 39A11
Keywords and Phrases: Second order, difference equation, damping term.
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