Distribution of the zeros of the solutions of hyperbolic differential equations with maxima

In this paper, the hyperbolic differential equation with maxima of the form u(tt) - [Delta u + mu(t)Delta u(x, t-tau)] + c(x, t, u(x, t), max(s is an element of[t-sigma, t]) u(x, s)) = f(x, t), where Omega is a bounded domain in R-n and tau, sigma = const > 0, are considered. Sufficient conditions for existence of zeros of the solutions of the problems considered in bounded domains are obtained.