The Bounded Variation Solutions For A Class Of Linear Ordinary Differential Equations

In this paper,the bounded variation solutions of the linear ordinary differential equations are discussed by combining the theory of function of bounded variation with linear ordinary diflferential equations.Farther,the variational stability for homogeneous linear ordinary differential equations is discussed.We do as follows:Firstly,some conceptions and lemmas to be applied are listed in this paper.Secondly,the global existence and uniqueness theorem of bounded variation solutions for linear ordinary differential equations is established.Thirdly,the fundamental matrix of homogeneous linear ordinary differential equations is discussed.Finally,the variational stability of trivial solution of homogeneous linear ordinary differential equations and the relation of variational stability between non-homogeneous and homogeneous linear ordinary differential equations are discussed.