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Conditions for existence and uniqueness of solutions to multipoint boundary value problems for systems of generalized ordinary differential equations. (English) Zbl 0902.34013
The paper is devoted to multipoint boundary value problems for systems of generalized ordinary differential equations \[ dx(t)= dA(t)\cdot f(t, x(t)),\tag{1} \]
\[ x_i(t_i)= \varphi_i(x),\quad i= 1,\dots, n,\tag{2} \] whith \([a,b]\subset \mathbb{R}\), \(t_1,\dots, t_n\in [a,b]\), \(A: [a,b]\to \mathbb{R}^{n\times n}\) is a matrix function of bounded variation, \(f: [a,b]\times \mathbb{R}^n\to\mathbb{R}^n\) is a vector function satisfying Carathéodory conditions with respect to \(A\), \(\varphi_i: BV_s([a, b],\mathbb{R}^n)\to \mathbb{R}\), \(i= 1,\dots, n\), are continuous functionals (in general nonlinear) defined on the normed space of all vector functions of bounded variation with supremum norm.
The author proves theorems on the existence and uniqueness of solutions to the problem (1), (2) and presents for generalized differential equations results analogous to earlier ones which were proven for systems of ordinary differential equations.

MSC:
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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