Electron. J. Differential Equations, Vol. 2018 (2018), No. 96, pp. 1-9.

Oscillation for second-order differential equations with delay

Blanka Baculikova

Abstract:
We establishing monotonic properties of non-oscillatory solutions, and oscillation criteria for the second-order delay differential equation
$$ y''(t)+p(t)y(\tau(t))=0. $$
The criteria obtained fulfil the gap in the oscillation theory and essentially improves the earlier ones. The progress is illustrated via Euler's differential equation. Moreover, we provide upper and lower bounds for the non-oscillatory solutions.

Submitted March 28, 2018. Published April 24, 2018.
Math Subject Classifications: 34K11, 34C10.
Key Words: Second order differential equation; delay argument; oscillation; monotonic properties.

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Blanka Baculikova
Department of Mathematics
Faculty of Electrical Engineering and Informatics
Technical University of Kosice
Letna; 9, 042 00~Kosice, Slovakia
email: blanka.baculikova@tuke.sk

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