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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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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 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |