Oscillation for First Order Superlinear Delay Differential Equations

Abstract

Some almost sharp sufficient conditions of oscillation and nonoscillation are obtained for the superlinear delay differential equation

Comparison Theorems on the Oscillation and Asymptotic Behaviour of Higher-Order Neutral Differential Equations

“…For such type of equations, one can easily relate oscillatory and/or almost-oscillatory nature of (13) with the same type of first-order equations. The readers may find oscillation results for sub-linear and/or super-linear in [7,[22][23][24]] to give explicit results on (13). Finally, we would like to point out that [2, Theorems 3 and 4] are not always true; indeed these results always hold only for strictly homogeneous equations (the authors need to assume that the forcing term is eventually non-negative and tends to zero at infinity when giving the proof for eventually negative solutions), and [ …”

Eventually positive solutions of first order nonlinear differential equations with a deviating argument

“…(See [8], [9], [10] or [11].) For equation (1.10) with γ = α, we can not apply Theorems 1.5 and D. However we can conclude that (1.10) with γ = α has no eventually positive solution, by the following result.…”

“…However, recently, Tang ([9], [10]) established very sharp sufficient conditions for P = ∅. They are very interesting, important and general.…”

Oscillation for higher order superlinear delay differential equations with unstable type

“…Motivated by the works of Tang [4,5] and Chen et al [1], in this paper we first prove that Eq. (1.2) always has either unbounded and nonoscillatory solution as Eq.…”

“…In the present paper, we consider the n-order superlinear delay differential equation with unstable type [4,5] studied the oscillation of the first order superlinear delay differential equation and obtained some "almost sharp" oscillation criteria. Motivated by the works of Tang [4,5] and Chen et al [1], in this paper we first prove that Eq.…”