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

Abstract

This paper is concerned with the oscillatory behavior of solutions to a class of second-order linear neutral differential equations with damping term. New sufficient conditions for the oscillation of all solutions are established that are not covered by existing results in the literature. Examples are also provided to illustrate the theorems.

Oscillation Criteria for Third‐Order Emden–Fowler Differential Equations with Unbounded Neutral Coefficients

“…For instance, for ≥ 2, if ( ) = − 1/ , then ( ) > 0, ( ) < 0, and ( ) < ( ), and so the function does not satisfy the conclusion of Lemma 1 provided that there is no ∈ (0, 1). On the basis of Lemma 1, one can easily revisit the results reported in [26][27][28].…”

New Criteria for Sharp Oscillation of Second-Order Neutral Delay Differential Equations

“…The methods mostly used in investigating the oscillatory behavior of (1) have been based on a reduction of order and comparison with oscillation of first-order delay differential equations, or on reducing (1) to a first-order Riccati inequality, based on a suitable Riccati type substitution, see e.g., [17] for more details. We note that none of the related results [3][4][5][6][7]10,[12][13][14][15][16][17][18][20][21][22]26,[28][29][30][31][32][33][34][35][36]39,42,46] involving (1) with α = 1, r(t) = 1, p(t) = 0, gives a sharp result when applied to the Euler linear delay differential equation…”

On the Oscillatory Properties of Solutions of Second-Order Damped Delay Differential Equations

“…Theorem 3. [23] Assume that σ(l) ≤ τ(l) and ( 8) hold. If there exists a positive function ρ ∈ C 1 ([l 0 , ∞), R + ) such that lim sup…”