MMN-4885
Oscillatory properties of fourth-order neutral differential equations using new monotonic properties
Kannan Suresh; Ganesh Purushothaman; John R. Graef; Ethiraju Thandapani;Abstract
The authors investigate the asymptotic behavior of solutions of the fourth-order half-linear neutral differential equation
\begin{equation} \label{e}
\tag{e}
(\alpha(t)((\mu(t)+d(t)\mu(a(t)))''')^b)'+m(t)\mu^b(\delta(t))=0
\end{equation}
without assuming $\alpha'(t)\geq 0$. By using a linearization method and deriving some new monotonic properties of the nonoscillatory solutions, they analyze the oscillatory behavior of solutions of \eqref{e}. They use two different techniques, namely, a comparison with second-order delay differential inequalities, and a generalization of very effective Koplatadze's method. They illustrate the improvements over known results by providing specific examples.
Vol. 26 (2025), No. 2, pp. 1029-1044