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On the oscillation of third-order quasi-linear delay differential equations. (English) Zbl 1265.34235

The aim of this work is to study asymptotic properties of the third-order quasi-linear delay differential equation \[ \biggl [a(t)\Bigl (x''(t)\Bigr)^{\alpha }\biggr ]'+q(t)x^{\alpha }\bigl (\tau (t)\bigr)=0\,, \tag{E} \] where \(\alpha >0\), \(\int _{t_0}^\infty {\frac {1}{a^{1/\alpha }(t)}\; {\operatorname {d}}t}<\infty \) and \(\tau (t)\leq t\). The authors establish a new condition which guarantees that every solution of (E) is either oscillatory or converges to zero. These results improve some known results in the literature. An example is given to illustrate the main results.

MSC:

34K11 Oscillation theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations

Citations:

Zbl 0954.34002
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