Oscillation of the solutions of impulsive hyperbolic equations with delay (Q1883954)

The paper deals with the oscillation of solutions of impulsive hyperbolic equations with delay \[ u_{tt}(t,x) = a(t) \Delta u(t,x) - p(t,x)f(u(t-\tau,x)), \quad t \neq t_k, \] subject to a Robin boundary condition. The author uses averaging technique to reduce the \(n\)-dimensional problem to a 1-dimensional one and studies the respective impulsive ordinary differential functional inequalities. The result obtained is illustrated by an example.