Electron. J. Differential Equations, Vol. 2016 (2016), No. 244, pp. 1-10.

Oscillation and Property B for third-order differential equations with advanced arguments

Blanka Baculikova, Jozef Dzurina

Abstract:
We establish sufficient conditions for the third-order nonlinear advanced differential equation
$$ \Big(a(t)[\big(b(t)y'(t)\big)']^{\gamma}\Big)'-p(t)f(y(\sigma(t)))=0 $$
to have property B or to be oscillatory. These conditions are based on monotonic properties and estimates of non-oscillatory solutions, and essentially improve known results for differential equations with deviating arguments and for ordinary differential equations.

Submitted March 15, 2016. Published September 7, 2016.
Math Subject Classifications: 34C10, 34K11.
Key Words: Third-order functional differential equation; Property B; advanced argument.

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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
Jozef Dzurina
Department of Mathematics
Faculty of Electrical Engineering and Informatics
Technical University of Kosice
Letna 9, 042 00 Kosice, Slovakia
email: jozef.dzurina@tuke.sk

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