Критические случаи устойчивости в системах с импульсным воздействием

The problem of stability of the zero solution of a nonlinear system of ordinary differential equations with impulse perturbation at fixed moments in a critical case is considered. To study the problem we suggest a new approach based on construction of discontinuous Lyapunov functions. The system of the second order with a cubic nonlinearity is studied on stability by this new approach.