Oscillation and asymptotic behavior of third-order nonlinear delay differential equations with positive and negative terms (Q2143491)

The authors are concerned with studying oscillation and non-oscillation in third-order delay differential equations with positive and negative terms. The main features of the paper are that the authors give a Kiguradze lemma and some a priori estimates; they establish a variety of oscillation theorems, including a Leighton-Wintner theorem, and Kamenev-type oscillation criteria. Finally, they provide necessary and sufficient conditions to guarantee that the positive solution \(x(t) > 0\) is bounded and tends to zero. The results are illustrated by examples.