Two (Multi) Point Nonlinear Lyapunov Systems Associated with an nth Order Nonlinear System of Differential Equations - Existence and Uniqueness
Murty, Kanuri N.
Howell, Gary W.
Sarma, G. V R L
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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.