**
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: ` 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 (MSC2000):** 34K10, 34K06

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2005 ELibM and
FIZ Karlsruhe / Zentralblatt MATH
for the EMIS Electronic Edition
*