MATHEMATICA BOHEMICA, Vol. 139, No. 4, pp. 649-655, 2014

Oscillation of the third order Euler differential equation with delay

Blanka Baculíková, Jozef Džurina

B. Baculíková, J. Džurina, Department of Mathematics, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Letná 9, 042 00 Košice, Slovakia, e-mail: blanka.baculikova@tuke.sk, jozef.dzurina@tuke.sk

Abstract: In the paper we offer criteria for oscillation of the third order Euler differential equation with delay
y"'(t)+\frac{k^2}{t^3}y(ct)=0.
We provide detail analysis of the properties of this equation, we fill the gap in the oscillation theory and provide necessary and sufficient conditions for oscillation of equation considered.

Keywords: third-order functional differential equation; Euler equation; oscillation; nonoscillation

Classification (MSC 2010): 34K11, 34C10


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