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Oscillation of third-order neutral differential equations. (English) Zbl 1201.34097

Summary: The objective of this paper is to study asymptotic properties of the couple of third-order neutral differential equations

[a(t)([x(t)±p(t)x(δ(t))] '' ) γ ] ' +q(t)x γ (τ(t))=0,tt 0 (E ± )

where a(t),q(t),p(t) are positive functions, γ>0 is a quotient of odd positive integers and τ(t)t,δ(t)t. We will establish some sufficient conditions which ensure that all nonoscillatory solutions of (E ± ) converge to zero. Some examples are considered to illustrate the main results.

34K11Oscillation theory of functional-differential equations
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