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R. Hakl, Mathematical Institute, Czech Academy of Sciences, Zizkova 22, 616 62 Brno, Czech Republic, e-mail: hakl@ipm.cz; A. Lomtatidze, B. Puza, Department of Mathematical Analysis, Masaryk University, Janackovo nam. 2a, 662 95 Brno, Czech Republic, e-mail: bacho@math.muni.cz, puza@math.muni.cz
Abstract: The nonimprovable sufficient conditions for the unique solvability of the problem
u'(t)=\ell(u)(t)+q(t),\qquad u(a)=c,
where $\ell C(I;\Bbb R)\to L(I;\Bbb R)$ is a linear bounded operator, $q\in L(I;\Bbb R)$, $c\in\Bbb R$, 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 $a$.
Keywords: linear functional differential equations, differential equations with deviating arguments, initial value problems
Classification (MSC 2000): 34K10, 34K06
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