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Cubo (Temuco)

versión On-line ISSN 0719-0646


DIAGANA, Toka; EZZINBI, Khalil  y  MIRAOUI, Mohsen. Pseudo-Almost Periodic and Pseudo-Almost Automorphic Solutions to Some Evolution Equations Involving Theoretical Measure Theory. Cubo [online]. 2014, vol.16, n.2, pp.01-32. ISSN 0719-0646.

Motivated by the recent works by the first and the second named authors, in this paper we introduce the notion of doubly-weighted pseudo-almost periodicity (respectively, doubly-weighted pseudo-almost automorphy) using theoretical measure theory. Basic properties of these new spaces are studied. To illustrate our work, we study, under Acquistapace-Terreni conditions and exponential dichotomy, the existence of - pseudo almost periodic (respectively, -pseudo almost automorphic) solutions to some nonautonomous partial evolution equations in Banach spaces. A few illustrative examples will be discussed at the end of the paper.

Palabras clave : Evolution family; exponential dichotomy; Acquistapace-Terreni conditions; pseudo-almost periodic; pseudo-almost automorphic; evolution equation; nonautonomous equation; doubly-weighted pseudo-almost periodic; doubly-weighted pseudo-almost automorphy; -pseudo-almost periodicity; -pseudo-almost automorphy; neutral systems; positive measure.

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