Mathematical Problems in Engineering 
Volume 6 (2000), Issue 4, Pages 395-410
doi:10.1155/S1024123X00001393

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

Abstract

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.