Mathematical Problems in Engineering
Volume 6 (2000), Issue 4, Pages 395-410

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

K. N. Murty,1 G. W. Howell,1 and G. V. R. L. Sarma2

1Mathematical Sciences, Florida Institute of Technology, Melbourne 32901-6975, FL, USA
2Department of Applied Mathematics, Andhra University, Visakhapatnam 530003, India

Received 15 February 2000

Copyright © 2000 K. N. Murty et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.