Some new oscillation criteria of third-order half-linear neutral difference equations

Abstract

In this article, we introduce the oscillation of all solutions of third-order half-linear neutral difference equation(OSTOHLDE) ∆ (g(n)(∆(h(n)∆z(n))) α) + f (n)y α (n + 1) = 0, where z(n) = y(n) + e(n)y(n − k) and α is a ratio of odd positive integers(PI). Our results are new and complement to the existing ones.