Abstract. This paper discusses the oscillation of nonlinear hyperbolic equation with deviating arguments of the form $${\partial ^2u\over\partial t^2}=a(t)\Delta u +\sum_{i=1}^ma_i(t)\Delta u(x,\rho_i(t)) -\sum_{j=1}^kP_j(x,t)f_j(u(x,\sigma_j(t))),$$ $(x,t)\in\Omega \times(0,\infty )$, where $\Omega\subset {\msbm R}^n$ is a bounded domain with a piecewise smooth boundary, $u=u(x,t)$ and $\Delta $ is the Laplacian in Euclidean $n$-space ${\msbm R}^n$.

AMS Subject Classification (1991): 35B05, 35R10, 34K15

Keyword(s): nonlinear hyperbolic equation, deviating argument, oscillation

Received December 3, 1991. (Registered under 5539/2009.)