## Abstract and Applied Analysis

### On a boundary value problem for scalar linear functional differential equations

#### Abstract

Theorems on the Fredholm alternative and well-posedness of the linear boundary value problem $u'(t)=\ell(u)(t)+q(t)$, $h(u)=c$, where $\ell:C([a,b];\mathbb{R})\rightarrow L([a,b];\mathbb{R})$ and $h:C([a,b];\mathbb{R}) \rightarrow \mathbb{R}$ are linear bounded operators, $q\in L([a,b]; \mathbb{R})$, and $c\in \mathbb{R}$, are established even in the case when $\ell$ is not a strongly bounded operator. The question on the dimension of the solution space of the homogeneous equation $u'(t)=\ell(u)(t)$ is discussed as well.

#### Article information

Source
Abstr. Appl. Anal., Volume 2004, Number 1 (2004), 45-67.

Dates
First available in Project Euclid: 7 March 2004

https://projecteuclid.org/euclid.aaa/1078681596

Digital Object Identifier
doi:10.1155/S1085337504309061

Mathematical Reviews number (MathSciNet)
MR2058792

Zentralblatt MATH identifier
1048.34106

Subjects
Primary: 34K06: Linear functional-differential equations 34K10

#### Citation

Hakl, R.; Lomtatidze, A.; Stavroulakis, I. P. On a boundary value problem for scalar linear functional differential equations. Abstr. Appl. Anal. 2004 (2004), no. 1, 45--67. doi:10.1155/S1085337504309061. https://projecteuclid.org/euclid.aaa/1078681596