Oscillation of third-order functional differential equations

B. Baculikova, Technical University of Kosice, Kosice, Slovakia
J. Dzurina, Technical University of Kosice, Kosice, Slovakia

E. J. Qualitative Theory of Diff. Equ., No. 43. (2010), pp. 1-10.

Abstract: The aim of this paper is to study oscillatory and asymptotic properties of the third-order nonlinear delay differential equation
\begin{equation*}\label{E0}
\left[a(t)\left[x''(t)\right]^{\gamma}\right]'+q(t)f(x\left[\tau(t)\right])=0.
\tag{$E$}
\end{equation*}
Applying suitable comparison theorems we present new criteria for oscillation or certain asymptotic behavior of nonoscillatory solutions of {(\ref{E0})}. Obtained results essentially improve and complement earlier ones. Various examples are considered to illustrate the main results.

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