Oscillation criteria for third-order neutral differential equations with continuously distributed delay
نویسندگان
چکیده
منابع مشابه
Nonlinear oscillation of certain third-order neutral differential equation with distributed delay
The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicab...
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By a solution of (.) wemean a function y(t) ∈ C[ty,∞) which has the property r(t)y′(t) ∈ C[ty,∞) and r(t)(r(t)y′(t))′ ∈ C[ty,∞) and satisfies (.) on [ty,∞) for every t ≥ ty ≥ t. We restrict our attention to those solutions of (.) which exist on I and satisfy the condition sup{|x(t)| : t ≥ t} > for any t ≥ ty. We assume that (.) possesses such a solution. A solution y(t) of (...
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and Applied Analysis 3 Theorem 2.1. Assume that 1.4 holds, 0 ≤ p t ≤ p1 < 1. If for some function ρ ∈ C1 t0,∞ , 0,∞ , for all sufficiently large t1 ≥ t0 and for t3 > t2 > t1, one has lim sup t→∞ ∫ t t3 ⎛ ⎜⎝ρ s q s (1 − p τ s ) ∫τ s t2 (∫v t1 1/a u du/b v ) dv ∫s t1 1/a u du − a s ( ρ′ s )2 4ρ s ⎞ ⎟⎠ds ∞, 2.1 ∫∞
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2012
ISSN: 0893-9659
DOI: 10.1016/j.aml.2012.01.007