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

Baculíková, B.; Džurina, J.

Math. Comput. Modelling 52, No. 1-2, 215-226 (2010).

Summary: The objective of this paper is to study asymptotic properties of the couple of third-order neutral differential equations \[ [a(t)([x(t)\pm p(t)x(\delta(t))]'')^{\gamma}]'+q(t)x^\gamma(\tau(t))=0,\quad t\geq t_0\tag{\(E^\pm\)} \] where \(a(t), q(t), p(t)\) are positive functions, \(\gamma >0\) is a quotient of odd positive integers and \(\tau (t)\leq t, \delta (t)\leq t\). We will establish some sufficient conditions which ensure that all nonoscillatory solutions of \((E^{\pm })\) converge to zero. Some examples are considered to illustrate the main results.

MSC:

34K11

Oscillation theory of functional-differential equations

Keywords:

third-order neutral differential equations; oscillation; nonoscillation

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