Oscillation of Second Order Nonlinear Mixed Neutral Differential Equations with Distributed Deviating Arguments

On the oscillation of second-order half-linear functional differential equations with mixed neutral term

“…However, oscillation results for mixed neutral differential and dynamic equations are relatively scarce in the literature; some results can be found, for example, in [20][21][22][23][24][25][26][27][28][29][30][31][32], and the references cited therein. We would like to point out that the results obtained in [20][21][22][23][24][25][26][27][28][29][30][31][32] require both of p 1 and p 2 to be constants or bounded functions, and hence, the results established in these papers cannot be applied to the cases where lim t→∞ p 1 (t) = ∞ and /or lim t→∞ p 2 (t) = ∞. In view of the observations above, we wish to develop new sufficient conditions which can be applied to the cases where lim t→∞ p 1 (t) = ∞ and /or lim t→∞ p 2 (t) = ∞.…”

Philos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms

“…Tongxing Li et al [16,17], Yunsong Qi et al [18], Chenghui Zhang et al [19], Zhenlai Han et al [20], Ethiraj Thandapani et al [21,22], Jianga et al [23], considered nonlinear second/third-order mixed neutral differential equations.…”

Oscillation results for second order half-linear functional dynamic equations with unbounded neutral coefficients on time scales

“…Since it has some direct applications in science, the oscillatory behavior of equation (1.1) and it's special and more general forms have been studied by numerous authors utilizing di¤erent methods. In reviewing the related literature, most of such results are concerned with the cases where the functions p j (t) are constant or bounded functions, for j = 1; 2; see for example [6,10,12,16,19,23,28,30,36,37] and the references cited therein. However, to the best of our knowledge, there does not appear to be any oscillation results for second order mixed neutral dynamic equations in the case where the neutral term includes unbounded neutral coe¢ cients.…”

“…Remark 4.1. Note that oscillation results presented in [6,10,12,16,19,23,28,30,36,37] fail to apply to the equations (4.1), (4.3), (4.5) and (4.7).…”