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On the solvability of nonlinear boundary value problems for functional-differential equations. (English) Zbl 0909.34057
The boundary value problem ${dx(t)\over dt}= p(x,x)(t)+ q(x)(t),\tag{1}$
$l(x,x)=c(x),\tag{2}$ is investigated where $$p: C(I,\mathbb{R}^n)\times C(I,\mathbb{R}^n)\to L(I, \mathbb{R}^n)$$, $$q: C(I, \mathbb{R}^n)\to L(I, \mathbb{R}^n)$$, $$l: C(I, \mathbb{R}^n)\times C(I, \mathbb{R}^n)\to \mathbb{R}^n$$, and $$c: C(I,\mathbb{R}^n)\to \mathbb{R}^n$$ are continuous operators, $$I= [a,b]$$, and $$p(x,.)$$ and $$l(x,.)$$ are linear operators for any fixed $$x\in C(I, \mathbb{R}^n)$$. Sufficient conditions for the existence of a solution to (1), (2) are established. A special case of (1), (2) is investigated.

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