\(H\)-oscillation of solutions of certain vector hyperbolic differential equations with deviating arguments (Q702610)

The paper deals with the following nonlocal vector hyperbolic equation \[ \begin{multlined} \frac{\partial^2}{\partial t^2}U(x,t) = a(t)\Delta U(x,t) + \sum_{k=1}^mb_k(t)\Delta U(x,\tau_k(t)) - p(x,t)U(x,t)\\- \sum_{h=1}^l \int_a^b q_h(x,t,\xi)U(x,g_h(t,\xi))\,d \sigma(\xi)+ F(x,t), \quad (x,t) \in \Omega \times [0,\infty) \end{multlined} \] subject either to homogeneous Dirichlet or non-homogeneous Neumann boundary conditions. The authors obtain criteria for \(H\)-oscillations of the solutions.