MATHEMATICA BOHEMICA, Vol. 127, No. 4, pp. 509-524 (2002)

New optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

R. Hakl, A. Lomtatidze, B. Puza

R. Hakl, Mathematical Institute, Czech Academy of Sciences, Zizkova 22, 616 62 Brno, Czech Republic, e-mail:
A. Lomtatidze, B. Puza, Department of Mathematical Analysis, Masaryk University, Janackovo nam. 2a, 662 95 Brno, Czech Republic, e-mail:,

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 (MSC2000): 34K10, 34K06

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