Oscillatory criteria of nonlinear hyperbolic equations with continuous deviating arguments (Q1569109)

The author studies the oscillation of solutions of the following nonlinear hyperbolic equations with continuous deviating arguments \[ \frac{\partial ^2}{\partial t^2} [u + \lambda (t)u(x,t-\tau)] = a(t)\Delta u - c(t,x,u) - \int_a^b q(x,t,\xi) u[x,g(t,\xi)]d \sigma (\xi) \] together with boundary conditions of Dirichlet or mixed types. Using averaging technique sufficient conditions for the oscillation are obtained. Examples are presented.