On existence and continuation of solutions of the state-dependent impulsive dynamical system with boundary constraints

Abstract

Abstract The state-dependent impulsive dynamical system with boundary constraints is a kind of special but common system in nature. But because of the complexity of the geometry or topological structures of the impulsive surface, it is hard to determine when an event or an impulsive surface is reached. Therefore, a general state-dependent impulsive nonlinear dynamical system is rarely studied. This paper presents a class of state-dependent impulsive dynamical systems with boundary constraints. We obtain the existence and continuation of their viable solutions and provide sufficient conditions for the existence and uniqueness of the viable solutions to the system. Finally, two examples are given to illustrate the effectiveness of the results