Sufficient conditions of oscillation of solutions to one class of neutral differential equations

V. V. Bashurov

Lomonosov Moscow State University

Abstract: In this paper, we establish oscillation conditions for a second-order neutral differential equation
\begin{equation*} \big(y -py_\tau \big)''+q(t)f(y_\sigma)=0, \quad y_\delta(t) \equiv y(t-\delta), \quad \delta \in \mathbb{R}. \end{equation*}
We prove sufficient conditions that guarantee the oscillation of solutions depending on the type of nonlinearity of the function $f$.

Keywords: neutral equation, delayed argument, oscillation

UDC: 517.929.8

MSC: 34K40

DOI: 10.36535/2782-4438-2025-245-16-23