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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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