Pulse phenomena of second-order impulsive differential equations with variable moments (Q597259)

The authors consider the following second-order impulsive differential equation with variable moments \[ \begin{cases} x''= -f(t,x,x'),\quad & t\neq\tau(x),\\ x(t+ 0)= h(x(t)),\quad & t=\tau(x),\\ x'(t+ 0)= g(x(t), x'(t)),\quad & t=\tau(x),\\ x(0)= x_0,\;x'(0)= y_0.\end{cases}\tag{1} \] Sufficient conditions for the solution \(x\) of (1) to meet the surface \(t=\tau(x)\) are derived.