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Solvability conditions for a nonlocal boundary value problem for linear functional differential equations. (English) Zbl 1207.34079

Summary: The aim of the paper is to find sufficient conditions for the unique solvability of the problem
\[ u'(t)=l(u)(t)+q(t),\quad u(a)=h(u)+c, \]
where \(l:C([a,b];\mathbb R)\to L([a,b];\mathbb R)\) and \(h:C([a,b];\mathbb R)\to\mathbb R\) are linear bounded operators, \(q\in L([a,b];\mathbb R)\), and \(c\in \mathbb R\).

MSC:

34K10 Boundary value problems for functional-differential equations
34K06 Linear functional-differential equations
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