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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| 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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| _version_ | 1832563123375046656 |
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| author | Jun Zhang Ti-Jun Xiao Jin Liang |
| author_facet | Jun Zhang Ti-Jun Xiao Jin Liang |
| author_sort | Jun Zhang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ec1cfb0ab7714a3a9dffcc5cb3ca2b04 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ec1cfb0ab7714a3a9dffcc5cb3ca2b042025-02-03T01:20:59ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/179525179525Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution EquationsJun Zhang0Ti-Jun Xiao1Jin Liang2School of Mathematics and Statistics, Central China Normal University, Hubei, Wuhan 430079, ChinaShanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan University, Shanghai 200433, ChinaDepartment of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, ChinaWe 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.http://dx.doi.org/10.1155/2012/179525 |
| spellingShingle | Jun Zhang Ti-Jun Xiao Jin Liang Weighted Pseudo Almost-Periodic Functions and Applications to Semilinear Evolution Equations Abstract and Applied Analysis |
| title | Weighted Pseudo Almost-Periodic Functions and
Applications to Semilinear Evolution Equations |
| title_full | Weighted Pseudo Almost-Periodic Functions and
Applications to Semilinear Evolution Equations |
| title_fullStr | Weighted Pseudo Almost-Periodic Functions and
Applications to Semilinear Evolution Equations |
| title_full_unstemmed | Weighted Pseudo Almost-Periodic Functions and
Applications to Semilinear Evolution Equations |
| title_short | Weighted Pseudo Almost-Periodic Functions and
Applications to Semilinear Evolution Equations |
| title_sort | weighted pseudo almost periodic functions and applications to semilinear evolution equations |
| url | http://dx.doi.org/10.1155/2012/179525 |
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