On the Solution of the Boundary Value Problem of First Order Lyapunov System of Differential Equations

AUTHOR(S):

Yan Wu

TITLE

On the Solution of the Boundary Value Problem of First Order Lyapunov System of Differential Equations

ABSTRACT

In this paper, we present results on the existence and uniqueness of a solution to the first order non-homogeneous Lyapunov system of differential equations satisfying general two-point boundary conditions. A variation of parameters type of formula is derived to construct an integral form of the solution. The uniqueness of the solution is established through the least squares solution of a double-sided matrix equation associated with the boundary value problem.

KEYWORDS

Fundamental matrix solution; Lyapunov equation; Variation of Parameters; Green’s matrix; Best least squares solution; Kronecker product

Cite this paper

Yan Wu . (2025) On the Solution of the Boundary Value Problem of First Order Lyapunov System of Differential Equations. International Journal of Mathematical and Computational Methods, 10, 240-245