Improved oscillation conditions for third-order neutral type difference equations

Abstract

<p>In this article, we study the oscillatory behavior of the third-order neutral type difference equation</p> <pre>∆(α_n(∆²(x_n + p_nx_n-k))^α) + q_nƒ(x_n-l) = 0</pre> <p>where α > 0, α_n > 0, q_n ≥ 0 and 0 ≤ p_n ≤ p < ∞. By using generalized Ricatti type transformation we present some new criteria which ensure that every solution is oscillatory. Also we provide examples that illustrate the importance of our results.</p>