Forced oscillation for impulsive hyperbolic boundary value problems with delay (Q702628)

The paper deals with forced oscillation of solutions of the impulsive hyperbolic equation with delay \[ u_{tt} (t,x) = a(t) \Delta u(t,x) + b(t) \Delta u(t-\sigma,x) - p(t,x)u(t,x) \] \[ - q(t,x)f[u(t-r,x)] + g(t,x), \quad t \neq t_k, \] subject to impulsive conditions for \(u\) and \(u_t\) at fixed moments of time \(\{t_k\}\), \(0 < t_1 < t_2 < ... < t_k < ...\), such that \(\lim_{k \to \infty} t_k = \infty\) and boundary condition either of Dirichlet or Robin type. The authors obtain sufficient conditions for forced oscillations using the averaging technique and Robin eigenfunction method.