In this paper, the oscillatory and nonoscillatory qualities for every solution of fourth-order neutral delay equation are discussed. Some conditions are established to ensure that all solutions are either oscillatory or approach to zero as .  Two examples are provided to demonstrate the obtained findings.

No abstract

No abstract

The asymptotic behavior for all nonoscillatory solutions for nonlinear neutral difference equations of third order has been investigated in this paper. Some necessary and sufficient conditions were obtained to ensure that these solutions are convergent to zero or divergent. There are some examples which illustrate our main findings.

This work led to find the invariant factors of the tenser product ( ξ* (C α 3 )) and prove the general formula of ℌ ( κ ⊗ ( ≡ * ( C α 3 ) ) )