On the mild solutions of higher-order differential equations in Banach spaces
For the higher-order abstract differential equation u(n)(t)=Au(t)+f(t), t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ℳ of BUC(ℝ,E) with respect to the above-mentioned equation in terms of solvability of the opera...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503303057 |
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| Summary: | For the higher-order abstract differential equation u(n)(t)=Au(t)+f(t), t∈ℝ, we give a new definition of mild solutions. We then characterize the regular admissibility of a translation-invariant subspace ℳ of BUC(ℝ,E) with respect to the above-mentioned equation in terms of solvability of the operator equation AX−X𝒟n=C. As applications, periodicity and almost periodicity of mild solutions are also proved. |
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| ISSN: | 1085-3375 1687-0409 |