Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces |
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Authors: | Ti-Jun Xiao Jin Liang Jun Zhang |
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Affiliation: | (1) Department of Mathematics, University of Science and Technology of China, Hefei, 230026, People’s Republic of China |
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Abstract: | In this paper, we prove that the space is complete. This not only gives an affirmative answer to a basic problem in this field, but also enables us to obtain an existence and uniqueness theorem of pseudo almost automorphic mild solutions to semilinear differential equations in Banach spaces. An example is given to illustrate our theorem. The work was supported partly by the National Natural Science Foundation of China, the NCET-04-0572 and Research Fund for the Key Program of the Chinese Academy of Sciences. |
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Keywords: | Vector-valued pseudo almost automorphic function Banach space Semilinear differential equation Abstract Cauchy problem |
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