Pulse accumulation in impulsive differential equations with variable times (Q1378693)

The author introduces a quite interesting new definition in the theory of differential equations with impulses: the pulse accumulation point, which appears when a solution undergoes an infinite number of pulses which accumulates as we tend to a finite time \(t^{*}\). This new phenomenon reveals as a distinctive characteristic of the impulsive differential equations in relation to classical differential equations. The paper contains a necessary condition for a point \(x^{*}\) to be a pulse accumulation point. Then some additional conditions are found to guarantee the existence of such a point. Some remarks on the possible continuation of the solutions of a differential equation with impulses after a pulse accumulation point are also provided.