Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution Equations
We first give a solution to a key problem concerning the completeness of the space of weighted pseudo almost-periodic functions and then establish a new composition theorem with respect to these functions. Some important remarks with concrete examples are also presented. Moreover, we prove an existe...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/179525 |
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| Summary: | We first give a solution to a key problem concerning the completeness
of the space of weighted pseudo almost-periodic functions and then establish a new
composition theorem with respect to these functions. Some important remarks with
concrete examples are also presented. Moreover, we prove an existence theorem for the
weighted pseudo almost-periodic mild solution to the semilinear evolution equation:
x′(t)=Ax(t)+f(t,x(t)), t∈ℝ,
where A is the infinitesimal generator of an exponentially stable C0-semigroup. An application is also given to illustrate the abstract existence theorem. |
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| ISSN: | 1085-3375 1687-0409 |