Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations. (English) Zbl 1023.34055

Summary: In some sense nonimprovably sufficient conditions guaranteeing the unique solvability of the problem \[ u'(t)= \ell (u)(t)+q(t), \quad u(a)=c, \] where \(\ell : C(I, \mathbb{R}) \to L(I, \mathbb{R})\) is a linear bounded operator, \(q \in L(I, \mathbb{R})\), and \(c \in \mathbb{R}\), are established.


34K06 Linear functional-differential equations
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