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On boundary value problems for functional-differential equations. (English) Zbl 0909.34054
A general theorem (the principle of a priori boundedness) on solvability of the boundary value problem $\frac{dx(t)}{dt}=f(x)(t),\qquad h(t)=0,$ is established, where $f: C([a,b]);\mathbb{R}^n)\to L([a,b]);\mathbb{R}^n),\qquad h: C([a,b]);\mathbb{R}^n)\to \mathbb{R}^n$ are continuous operators. As an application, effective criteria for the solvability of the boundary value problem $\frac{dx(t)}{dt}=f_0(t,x(t)),$
$x(t_1(x))=A(x)x(t_2(x))+c_0,$ are obtained, where $$f_0: I=[a,b] \times \mathbb{R}^n\to \mathbb{R}^n$$ is a vector function satisfying local Carathéodory conditions, $$c_0\in \mathbb{R}^n$$ and $$t_i: C(I,\mathbb{R}^n)\to I$$, $$i=1,2$$, $$A: C(I,\mathbb{R}^n)\to \mathbb{R}^n$$ are continuous operators.
Reviewer: J.Diblík (Brno)

##### MSC:
 34K10 Boundary value problems for functional-differential equations
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