Pseudo-almost Periodic and Pseudo-almost Automorphic Solutions to Evolution Equations in Hilbert Spaces

In this work we prove some existence and uniqueness results for pseudo-almost periodic and pseudo-almost automorphic solutions to a class of semi-linear differential equations in Hilbert spaces using theoretical measure theory. The main technique is based upon some appropriate composition theorems c...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2016-04, Vol.13 (2), p.703-717
Main Authors: Salah, Mounir Ben, Ezzinbi, Khalil, Rebey, Amor
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:In this work we prove some existence and uniqueness results for pseudo-almost periodic and pseudo-almost automorphic solutions to a class of semi-linear differential equations in Hilbert spaces using theoretical measure theory. The main technique is based upon some appropriate composition theorems combined with the Banach contraction mapping principle and the method of the invariant subspaces for unbounded linear operators. A few illustrative examples will be discussed at the end of the paper.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-014-0510-2