Oscillation of hyperbolic partial differential equations with impulses
This is an interesting paper which deals with the oscillation of solutions of impulsive hyperbolic equations \[ u_{tt}(t,x) = a(t) \Delta u(t,x) - p(t,x)u(t,x), \quad t \neq t_k, x \in \Omega, \] together with the boundary condition \[ \frac{\partial u}{\partial n} (t,x) + \gamma (t,x) u(t,x) = 0, \quad t \neq t_k, x \in \partial \Omega \] and the impulsive condition \[ u(t_k^+,x) = g(t_k,x,u(t_k,x)), \quad x \in \bar{\Omega}, \;k = 1,2,\dots , \] where \(t_1 < t_2 < \dots < t_k < \dots \) are given numbers such that \(\lim_{k \to \infty} t_k = \infty\). The author obtains sufficient conditions for oscillation of the solution using averaging technique and considering adequate impulsive ordinary differential inequalities.
scientific article; zbMATH DE number 1861256