## 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.

### MSC:

 34K06 Linear functional-differential equations
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### References:

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