Oscillatory behavior of second order damped neutral differential equations with distributed deviating arguments

Abstract

The authors establish some new criteria for the oscillation of second order damped nonlinear neutral differential equations with distributed deviating arguments. Two examples are also provided to illustrate the results.

New criteria for oscillation of nonlinear neutral differential equations

“…In the case where γ ≤ β, using the facts u(t) > 0 and u (t) > 0, we have u(t) ≥ B > 0 for t sufficiently large. It follows from (2.4) and (2.7) that 17) where C = min{A, B}. The rest of the proof is similar to that of Theorem 2.1 and so we omit it.…”

On Oscillation of Second-Order Linear Neutral Differential Equations With Damping Term

“…In recent years, there has been a great interest in investigating the oscillatory behavior of solutions of various classes of second order neutral differential equations without damping term, and we refer the reader to the papers [2,3,4,5,8,11,12,13,14,16,17,18,19,21] and the references therein as examples of recent results on this topic. However, determining oscillation criteria for second-order neutral differential equations with damping term has not received a great deal of attention in the literature; moreover, the results obtained are for the cases 0 < p(t) ≤ p 0 < 1 or −1 < p 0 ≤ p(t) < 0, see the papers [7,9,20] as example. This means that the results obtained in these papers cannot be applied to the case where p(t) → ∞ as t → ∞.…”

Oscillatory Behavior of Second-Order Half-Linear Neutral Differential Equations with Damping

“…For some typical results, we refer the reader to [2][3][4]7,8,[10][11][12][15][16][17][18][19][20]23] and the references cited therein as examples of recent results on this topic. However, results on the oscillatory behavior of solutions of second-order neutral differential equations with damping term are relatively scarce in the literature; some results can be found, for example, in [5,6,21,22]. It should be noted that although papers [5,6,21,22] deal with second-order neutral differential equations with damping term, the results obtained in these papers except [22] cannot be applied to the case where h(t) → ∞ as t → ∞.…”

“…However, results on the oscillatory behavior of solutions of second-order neutral differential equations with damping term are relatively scarce in the literature; some results can be found, for example, in [5,6,21,22]. It should be noted that although papers [5,6,21,22] deal with second-order neutral differential equations with damping term, the results obtained in these papers except [22] cannot be applied to the case where h(t) → ∞ as t → ∞. Motivated by the above observations, here we wish to develop sufficient conditions for equation (1.1) to be oscillatory in the case where h(t) > 1 and/or h(t) → ∞ as t → ∞.…”