Two (multi) point nonlinear Lyapunov systems associated with an nth order nonlinear system of differential equations - Existence and uniqueness

This paper presents a criterion for the existence and uniqueness of solutio ns to two and multipoint boundary value problems associated with an nth ord er nonlinear Lyapunov system. A variation of parameters formula is develope d and used as a tool to obtain existence and uniqueness. We discuss solutio n of the second order problem by the ADI method and develop a fixed point m ethod to find the general solution of the nth order Lyapunov system. The re sults of Barnett (SIAM J. Appl. Anal. 24(1), 1973) are a particular case.