Qualitative properties of nonlinear difference systems

摘要

This paper gives criteria for the existence and uniqueness of solutions to two and multipoint boundary value problems associated with a typical system of kth order nonlinear Lyapunov system. A variation of parameters formula for nonlinear kth order system is established. Using this formula, we also study various concepts of stability and establish sufficient conditions for the kth order difference system to be Lipschitz stable and uniform Lipschitz stable.