On a boundary value problem for scalar linear functional differential equationsReport as inadecuate




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Abstract and Applied Analysis - Volume 2004 2004, Issue 1, Pages 45-67



Mathematical Institute, Czech Academy of Sciences, Brno 616 62, Czech Republic

Department of Mathematical Analysis, Faculty of Science, Masaryk University, Brno 66295, Czech Republic

Department of Mathematics, University of Ioannina, Ioannina 451 10, Greece

Received 24 July 2003

Copyright © 2004 Hindawi Publishing Corporation. 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=ℓut+qt, hu=c, where ℓ:Ca,b;ℝ→La,b;ℝ and h:Ca,b;ℝ→ℝ are linear bounded operators, q∈La,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=ℓut is discussed as well.





Author: R. Hakl, A. Lomtatidze, and I. P. Stavroulakis

Source: https://www.hindawi.com/



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