Oscillations of higher order neutral differential equations of mixed type

Oscillation results for second-order neutral differential equations of mixed type

“…The authors gave some oscillation criteria when n ≥ 1 is odd, c, C and Q are nonnegative real constants, and g, G, h, H, and q are positive real constants. It is easy to find that the results given in [26], [27] cannot be applied to Eq. (1.1).…”

“…G r a c e [26] and Y a n [27] obtained several sufficient conditions for the oscillation of solutions of higher order neutral functional differential equation of the form…”

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) = ∞.…”

Oscillation results for third order nonlinear neutral differential equations of mixed type

“…Recently there has been a great interest in studying the oscillatory and asymptotic behavior of third order differential equations, see for example [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23], and the references cited therein. In [1,4,7,8,9,15,20,23], the authors studied the oscillatory behavior of solutions of equation (1.1) when b(t) ≡ 0, c(t) ≡ 0 and p(t) ≡ 0.…”

“…In [5,6,10,11,17,18,19,21], the authors studied the oscillatory behavior of solutions of equation (1.1) when c(t) ≡ 0 and p(t) ≡ 0. In [2,13,14,22], the authors discussed the oscillatory behavior of all solutions of equation (1.1) when α = β = γ = 1.…”