Oscillation criteria of third-order neutral differential equations with damping and distributed deviating arguments

Our objective in this paper is to study the oscillatory and asymptotic behavior of the solutions of third-order neutral differential equations with damping and distributed deviating arguments. New oscillation criteria are established, which are based on a refinement generalized Riccati transformation. An important tool for this investigation is the integral averaging technique. Moreover, we provide an example to illustrate the main results.

Improved Oscillation Criteria for 2nd-Order Neutral Differential Equations with Distributed Deviating Arguments

In this study, we establish new sufficient conditions for oscillation of solutions of second-order neutral differential equations with distributed deviating arguments. By employing a refinement of the Riccati transformations and comparison principles, we obtain new oscillation criteria that complement and improve some results reported in the literature. Examples are provided to illustrate the main results.

Sufficient Conditions for Oscillation of Fourth-Order Neutral Differential Equations with Distributed Deviating Arguments

Some new sufficient conditions are established for the oscillation of fourth order neutral differential equations with continuously distributed delay of the form r t N x ‴ t α ′ + ∫ a b q t , ϑ x β δ t , ϑ d ϑ = 0 , where t ≥ t 0 and N x t : = x t + p t x φ t . An example is provided to show the importance of these results.