Oscillation theorems for hyperbolic equations of neutral type (Q2767754)

The authors consider hyperbolic equations of neutral type of the form: NEWLINE\[NEWLINE{\partial^2 \over\partial t^2}\bigl[u(x,t)+ p(t)u(x,t-\tau)\bigr]= a(t) \Delta u(x,t)-q(t) f\bigl(u(x,G(t) \bigr),\;(x,t)\in\Omega \times\mathbb{R}_+ \tag{1}NEWLINE\]NEWLINE with boundary conditions NEWLINE\[NEWLINE{\partial u\over\partial\nu} +\mu(x,t)u=0,\;(x,t)\in \partial \Omega\times\mathbb{R}_+ \tag{2}NEWLINE\]NEWLINE NEWLINE\[NEWLINEu=0,\quad (x,t)\in \partial \Omega \times \mathbb{R}_+, \tag{3}NEWLINE\]NEWLINE where \(\mathbb{R}_+= [0,\infty)\), \(\Omega\) is a bounded domain with piecewise smooth boundary \(\partial\Omega\), \(\mu(x,t)\) is a continuous and nonnegative function on \(\partial\Omega \times\mathbb{R}_+\), \(\nu\) denotes the unit exterior normal vector to \(\partial\Omega\). NEWLINENEWLINENEWLINEThe authors present oscillation criteria for (1), (2) and (1), (3) improving on the results of \textit{Y. Yu} and \textit{B. Cui} [Acta Math. Appl. Sin., Engl. Ed. 10, 102-106 (1994; Zbl 0829.35084)].