Oscillation criteria for the second-order linear advanced differential equations

On the half-line $\mathbb{R}_+=[0,+\infty[\,$, we consider the second-order linear differential equation with argument deviation \begin{equation*} \label{Oplustil:1}\tag{1} u''(t)+p(t)u(\sigma(t))=0, \end{equation*} where $p\colon\mathbb{R}_+\to\mathbb{R}_+$ is a locally Lebesgue integrable function and $\sigma\colon\mathbb{R}_+\to\mathbb{R}_+$ is a continuous function such that $\sigma(t)\geq t$, for $t\geq0$.
New oscillatory criteria are established for solutions to equation \eqref{Oplustil:1}. Riccati's technique and suitable estimates of non-oscillatory solutions are used for the proof of the obtained results. The presented criteria, in a certain sense, generalize those known from the theory of ordinary differential equations.