Notes on the oscillation for certain hyperbolic equations of neutral type (Q2726139)

The author's deal with the following nonlinear hyperbolic equations with continuous distributed deviating arguments NEWLINE\[NEWLINE{\partial^2 \over \partial t^2}\bigl[ u+\lambda(t) u(x,t-\tau) \bigr]=a(t) \Delta_xu-c (x,t,u)-\int^b_a q(x,t,\xi) u\bigl[x,g(t,\rho) \bigr]d\sigma (\xi)+f(x,t). \tag{1}NEWLINE\]NEWLINE With boundary condition (2) \({\partial u\over\partial n}= \psi(x,t)\) on \((x,t\in \partial\Omega \times\mathbb{R}_+\). Here \(\Delta\) is the Laplacian, \(\tau\) is a positive constant, \((x,t)\in \Omega\times\mathbb{R}_+\), \(\Omega\) is a bounded domain with a piecewise smooth boundary \(\partial\Omega\), \(\psi\) is a continuous function on \(\partial\Omega \times\mathbb{R}_+\), \(n\) denotes the unit exterior normal vector to \(\partial\Omega\). The goal of the authors is to establish some oscillatory criteria for (1), (2).