Abstract and Applied Analysis
Volume 2004 (2004), Issue 1, Pages 45-67
doi:10.1155/S1085337504309061
On a boundary value problem for scalar linear functional differential equations
1Mathematical Institute, Czech Academy of Sciences, Brno 616 62, Czech Republic
2Department of Mathematical Analysis, Faculty of Science, Masaryk University, Brno 66295, Czech Republic
3Department of Mathematics, University of Ioannina, Ioannina 451 10, Greece
Received 24 July 2003
Copyright © 2004 R. Hakl et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Theorems on the Fredholm alternative and well-posedness of the linear boundary value problem u′(t)=ℓ(u)(t)+q(t), h(u)=c, where ℓ:C([a,b];ℝ)→L([a,b];ℝ) and h:C([a,b];ℝ)→ℝ are linear bounded operators, q∈L([a,b];ℝ), and c∈ℝ, are established even in the case when ℓ is not a strongly bounded operator. The question on the dimension of the solution space of the homogeneous equation u′(t)=ℓ(u)(t) is discussed as well.