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

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, 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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