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New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations. (English) Zbl 1017.34065
Summary: Nonimprovable sufficient conditions for the unique solvability of the problem $u'(t)=\ell (u)(t)+q(t),\qquad u(a)=c,$ where $$\ell \: C(I;\mathbb{R})\to L(I;\mathbb{R})$$ is a linear bounded operator, $$q\in L(I;\mathbb{R})$$, $$c\in \mathbb{R}$$, are established which are different from known results. They are interesting especially in the case where the operator $$\ell$$ is not of Volterra’s type with respect to the point $$a$$.

##### MSC:
 34K05 General theory of functional-differential equations 34K06 Linear functional-differential equations
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