On a boundary value problem for scalar linear functional differential equations
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. T...
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Hindawi Limited
2004-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337504309061 |
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doaj-2715bb4d47944922b0eaa01a6fa28bd42020-11-24T23:18:00ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092004-01-0120041456710.1155/S1085337504309061On a boundary value problem for scalar linear functional differential equationsR. Hakl0A. Lomtatidze1I. P. Stavroulakis2Mathematical Institute, Czech Academy of Sciences, Brno 616 62, Czech RepublicDepartment of Mathematical Analysis, Faculty of Science, Masaryk University, Brno 66295, Czech RepublicDepartment of Mathematics, University of Ioannina, Ioannina 451 10, GreeceTheorems 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.http://dx.doi.org/10.1155/S1085337504309061 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
R. Hakl A. Lomtatidze I. P. Stavroulakis |
| spellingShingle |
R. Hakl A. Lomtatidze I. P. Stavroulakis On a boundary value problem for scalar linear functional differential equations Abstract and Applied Analysis |
| author_facet |
R. Hakl A. Lomtatidze I. P. Stavroulakis |
| author_sort |
R. Hakl |
| title |
On a boundary value problem for scalar linear functional differential equations |
| title_short |
On a boundary value problem for scalar linear functional differential equations |
| title_full |
On a boundary value problem for scalar linear functional differential equations |
| title_fullStr |
On a boundary value problem for scalar linear functional differential equations |
| title_full_unstemmed |
On a boundary value problem for scalar linear functional differential equations |
| title_sort |
on a boundary value problem for scalar linear functional differential equations |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2004-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/S1085337504309061 |
| work_keys_str_mv |
AT rhakl onaboundaryvalueproblemforscalarlinearfunctionaldifferentialequations AT alomtatidze onaboundaryvalueproblemforscalarlinearfunctionaldifferentialequations AT ipstavroulakis onaboundaryvalueproblemforscalarlinearfunctionaldifferentialequations |
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