Oscillatory Behavior of Second-Order Neutral Differential Equations
نویسندگان
چکیده
Abstract In this paper, we study oscillatory properties of neutral differential equations. Moreover, discuss some examples that show the effectiveness and feasibility main results.
منابع مشابه
Oscillatory Behavior of Second Order Neutral Differential Equations
Oscillation criteria are obtained for solutions of forced and unforced second order neutral differential equations with positive and negative coefficients. These criteria generalize those of Manojlović, Shoukaku, Tanigawa and Yoshida (2006).
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The authors establish some new criteria for the oscillation and asymptotic behavior of all solutions of the equation. (a(t)(x(t) + p(t)x(τ(t)))) + q(t) max [σ(t),t] x(s) = 0, t ≥ t0 ≥ 0, where a(t) > 0, q(t) ≥ 0, τ(t) ≤ t, σ(t) ≤ t, α is the ratio of odd positive integers, and ∫∞ 0 dt a(t) < ∞. Examples are included to illustrate the results. AMS Subject Classification: 34K11, 34K99
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(H) I := [t,∞), r,p ∈ C(I,R), r(t) > , and p(t)≥ ; (H) q ∈ C(I× [a,b], [,∞)) and q(t, ξ ) is not eventually zero on any [tμ,∞)× [a,b], tμ ∈ I; (H) g ∈ C(I× [a,b], [,∞)), lim inft→∞ g(t, ξ ) =∞, and g(t,a)≤ g(t, ξ ) for ξ ∈ [a,b]; (H) τ ∈ C(I,R), τ ′(t) > , limt→∞ τ (t) =∞, and g(τ (t), ξ ) = τ [g(t, ξ )]; (H) σ ∈ C([a,b],R) is nondecreasing and the integral of (.) is taken in the...
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ژورنال
عنوان ژورنال: Bulletin Of The Brazilian Mathematical Society, New Series
سال: 2021
ISSN: ['1678-7544', '1678-7714']
DOI: https://doi.org/10.1007/s00574-021-00276-3