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New oscillation criteria for third-order half-linear advanced differential equations. (English) Zbl 1474.34459

Summary: The theme of this article is to provide some sufficient conditions for the asymptotic property and oscillation of all solutions of third-order half-linear differential equations with advanced argument of the form \[({r_2} (t) (({r_1} (t) (y' (t))^\alpha)')^\beta)' + q (t){y^\gamma} (\sigma (t)) = 0, \;\; t \ge {t_0} > 0,\] where \({\int^\infty}{r_1^{-\frac{1}{\alpha}}} (s){\mathrm{d}}s < \infty\) and \({\int^\infty}{r_2^{-\frac{1}{\beta}}} (s){\mathrm{d}}s < \infty\). The criteria in this paper improve and complement some existing ones. The results are illustrated by two Euler-type differential equations.

MSC:

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