Mathematical Problems in Engineering
This paper presents a criterion for the existence and uniqueness of solutions to two and multipoint boundary value problems associated with an nth order nonlinear Lyapunov system. A variation of parameters formula is developed and used as a tool to obtain existence and uniqueness. We discuss solution of the second order problem by the ADI method and develop a fixed point method to find the general solution of the nth order Lyapunov system. The results of Barnett (SIAM J. Appl. Anal. 24(1), 1973) are a particular case.
Murty, K. N., Howell, G. W., & Sarma, G. V. R. L. (2000). Two (multi) point nonlinear lyapunov systems associated with an nth order nonlinear system of differential equations - existence and uniqueness. Mathematical Problems in Engineering, 6(4), 395-410.