Geodesic
Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations
Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 513-530

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Nonimprovable, in a sense sufficient conditions guaranteeing 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, $q\in L(I,\mathbb R)$, and $c\in \mathbb R$, are established.
Classification : 34K06, 34K10
Keywords: linear functional differential equations; Cauchy problem; existence and uniqueness; differential inequalities 
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     author = {Bravyi, E. and Hakl, R. and Lomtatidze, A.},
     title = {Optimal conditions for unique solvability of the {Cauchy} problem for first order linear functional differential equations},
     journal = {Czechoslovak Mathematical Journal},
     pages = {513--530},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {2002},
     mrnumber = {1923257},
     zbl = {1023.34055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2002__52_3_a5/}
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Bravyi, E.; Hakl, R.; Lomtatidze, A. Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations. Czechoslovak Mathematical Journal, Tome 52 (2002) no. 3, pp. 513-530. http://geodesic.mathdoc.fr/item/CMJ_2002__52_3_a5/