On Oscillatory and Asymptotic Behavior of a Second-Order Nonlinear Damped Neutral Differential Equation
نویسندگان
چکیده
منابع مشابه
On Oscillatory Nonlinear Second Order Neutral Delay Differential Equations
In this work, we investigate the oscillation criteria for second order neutral delay differential equations of the form (r(t)[y(t)+ p(t)y(δ (t))]′)′ +q(t)G(y(τ(t))) = 0 and (r(t)[[y(t)+ p(t)y(δ (t))]′]α )′ +q(t)(yβ (τ(t))) = 0, where α and β are the ratio of odd positive integers. Mathematics subject classification (2010): 34C10, 34C15.
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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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In this paper we find sufficient conditions for every solution of the neutral delay difference equation ∆(rn∆(yn − pnyn−m)) + qnG(yn−k) = 0 to oscillate or to tend to zero or ±∞ as n → ∞, where ∆ is the forward difference operator given by ∆xn = xn+1−xn, pn, qn, and rn are infinite sequences of real numbers with qn ≥ 0, rn > 0. Different ranges of {pn} are considered. This paper improves,genera...
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ژورنال
عنوان ژورنال: International Journal of Differential Equations
سال: 2016
ISSN: 1687-9643,1687-9651
DOI: 10.1155/2016/3746368