Electron. J. Diff. Equ., Vol. 2015 (2015), No. 70, pp. 1-10.

Oscillation of solutions to fourth-order trinomial delay differential equations

Jozef Dzurina, Blanka Baculikova, Irena Jadlovska

Abstract:
The objective of this article is to study the oscillation properties of the solutions to the fourth-order linear trinomial delay differential equation
$$ y^{(4)}(t)+p(t)y'(t)+q(t)y(\tau(t))=0. $$
Applying suitable comparison principles, we present new criteria for oscillation. In contrast with the existing results, we establish oscillation of all solutions, and essentially simplify the examination process for oscillation. An example is included to illustrate the importance of results obtained.

Submitted February 5, 2015. Published March 24, 2015.
Math Subject Classifications: 34C10, 34K11.
Key Words: Fourth-order functional differential equation; oscillation; delay argument; comparison theorem.

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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
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
Irena Jadlovska
Department of Mathematics
Faculty of Electrical Engineering and Informatics
Technical University of Kosice
Letna 9, 042 00 Kosice, Slovakia
email: irena.jadlovska@student.tuke.sk

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