Geodesic
New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations
Mathematica Bohemica, Tome 127 (2002) no. 4, pp. 509-524.

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The nonimprovable sufficient conditions for the unique solvability of the problem \[ u^{\prime }(t)=\ell (u)(t)+q(t),\qquad u(a)=c, \] where $\ell \: C(I;\mathbb{R})\rightarrow L(I;\mathbb{R})$ is a linear bounded operator, $q\in L(I;\mathbb{R})$, $c\in \mathbb{R}$, are established which are different from the previous results. More precisely, they are interesting especially in the case where the operator $\ell $ is not of Volterra’s type with respect to the point $a$.
DOI : 10.21136/MB.2002.133950
Classification : 34K05, 34K06, 34K10, 65L05
Keywords: linear functional differential equations; differential equations with deviating arguments; initial value problems 
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     title = {New optimal conditions for unique solvability of the {Cauchy} problem for first order linear functional differential equations},
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Hakl, R.; Lomtatidze, A.; Půža, B. New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations. Mathematica Bohemica, Tome 127 (2002) no. 4, pp. 509-524. doi : 10.21136/MB.2002.133950. http://geodesic.mathdoc.fr/articles/10.21136/MB.2002.133950/

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