Oscillation theorems for second order neutral differential equations

• Main Authors: Blanka Baculíková, Tongxing Li, Jozef Džurina
• Format: Article
• Language: English
• Published: University of Szeged 2011-09-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: second-order neutral differential equations; comparison theorem; oscillation.
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=569

In this paper new oscillation criteria for the second order neutral differential equations of the form \begin{equation*} \left(r(t)\left[x(t)+p(t)x(\tau(t))\right]'\right)'+q(t)x(\sigma(t))+v(t)x(\eta(t))=0 \tag{$E$}\end{equation*} are presented. Gained results are based on the new comparison theorems, that enable us to reduce the problem of the oscillation of the second order equation to the oscillation of the first order equation. Obtained comparison principles essentially simplify the examination of the studied equations. We cover all possible cases when arguments are delayed, advanced or mixed.