No abstract

The aim of this work is to study asymptotic properties of a class of fourth-order delay differential equations. Our results in this paper not only generalize some previous results, but also improve the earlier ones. Examples are considered to elucidate the main results.

This paper deals with the oscillation properties of higher-order nonlinear differential equations with distributed delay b()(y (n-1) ()) γ + d c q(, ξ)y γ (g(, ξ)) d(ξ) = 0, ≥ 0 , under the condition ∞ 0 1 b 1 γ () d < ∞. We obtain new oscillation criteria by employing a refinement of the generalized Riccati transformations and new comparison principles. We provide some examples to illustrate the main results.

Based on the comparison with first-order delay equations, we establish a new oscillation criterion for a class of even-order neutral differential equations. Our new criterion improves a number of existing ones. An illustrative example is provided.

In this work, new conditions are obtained for the oscillation of solutions of the even-order equation (r(ζ)z (n-1) (ζ)) + b a q(ζ , s)f (x(g(ζ , s))) ds = 0, ζ ≥ ζ 0 , where n ≥ 2 is an even integer and z(ζ) = x α (ζ) + p(ζ)x(σ (ζ)). By using the theory of comparison with first-order delay equations and the technique of Riccati transformation, we get two various conditions to ensure oscillation of solutions of this equation. Moreover, the importance of the obtained conditions is illustrated via some examples.