Conditions of Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for a System of Generalized Ordinary Differential Equations期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Conditions of Existence and Uniqueness of Solutions of the Multipoint Boundary Value Problem for a System of Generalized Ordinary Differential Equations

Authors:	Ashordia M

Abstract:	Effective sufficient conditions are established for the solvability and unique solvability of the boundary value problem $\begin{gathered} dx(t) = dA(t) \cdot f(t,x(t)), \hfill \\ x_i (t_i ) = \varphi _i (x){\text{ }}(i = 1,...,n), \hfill \\ \end{gathered}$ where $x = (x_i )_{i = 1}^n ,{\text{ }}A:a,b] \to R^{n \times n}$ is a matrix-function with bounded variation components, $f:a,b] \times R^n \to R^n$ is a vector-function belonging to the Carathéodory class corresponding to $A;t_1 ,...,t_n \in a,b]{\text{ and }}\varphi _1 ,...,\varphi _n$ are continuous functionals (in general nonlinear) defined on the set of all vector-functions of bounded variation.

Keywords:	Generalized ordinary differential equations multipoint boundary value problem solvability unique solvability
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