Ordinary differential equations/Partial differential equations
Almost automorphic evolution equations with compact almost automorphic solutions
Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1071-1077.

We prove that some almost automorphic evolution equations carry compact almost automorphic solutions. Moreover, we show that the almost automorphy of the coefficients is not necessary to obtain almost automorphic solutions. This improves the assumptions and the conclusion of a result of M. Zaki (Ann. Mat. Pura Appl. (4) 101 (1) (1974) 91–114), which gives the nature of solutions with relatively compact range for some almost automorphic evolution equations in Banach spaces. We note that many results in the literature can be improved in this direction.

Nous montrons que certaines équations d'évolution presque automorphes possèdent des solutions compactes presque automorphes. De plus, nous montrons que la presque automorphie des coefficients n'est pas nécessaire pour obtenir des solutions presque automorphes. Cela améliore les hypothèses et la conclusion d'un résultat de M. Zaki (Ann. Mat. Pura Appl. (4) 101 (1) (1974) 91–114), qui donne la nature des solutions avec image relativement compacte pour certaines équations d'évolution presque automorphes dans les espaces de Banach. Nous notons que de nombreux résultats dans la littérature peuvent être améliorés dans cette direction.

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DOI: 10.1016/j.crma.2016.10.001
Es-sebbar, Brahim 1

1 Université Cadi-Ayyad, Faculté des sciences Semlalia, Département de mathématiques, BP 2390, Marrakesh, Morocco
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Es-sebbar, Brahim. Almost automorphic evolution equations with compact almost automorphic solutions. Comptes Rendus. Mathématique, Volume 354 (2016) no. 11, pp. 1071-1077. doi : 10.1016/j.crma.2016.10.001. http://www.numdam.org/articles/10.1016/j.crma.2016.10.001/

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