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Zbl 1192.34073
Bartušek, Miroslav; Cecchi, Mariella; Došlá, Zuzana; Marini, Mauro
Oscillation for third-order nonlinear differential equations with deviating argument.
(English)
[J] Abstr. Appl. Anal. 2010, Article ID 278962, 19 p. (2010). ISSN 1085-3375; ISSN 1687-0409/e

Summary: We study necessary and sufficient conditions for the oscillation of the third-order nonlinear ordinary differential equation with damping term and deviating argument $$x'''(t)+q(t)x'(t)+r(t)f(x(\varphi(t)))=0.$$ Motivated by the work of {\it I. T. Kiguradze} [Differ. Uravn. 28, No. 2, 207--219 (1992; Zbl 0768.34018)], the existence and asymptotic properties of nonoscillatory solutions are investigated in case when the differential operator ${\cal L}x=x'''+q(t)x'$ is oscillatory.
MSC 2000:
*34K11 Oscillation theory of functional-differential equations

Citations: Zbl 0768.34018

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