Asymptotically almost automorphic solutions of dynamic equations on time scales

Carlos Lizama, Jaqueline G. Mesquita

DOI: http://dx.doi.org/10.12775/TMNA.2019.024

Abstract


In the present work, we introduce the concept of asymptotically almost automorphic functions on time scales and study their main properties. We study nonautonomous dynamic equations on time scales given by $x^{\Delta} (t) = A(t) x(t) + f(t)$ and $x^{\Delta} (t) = A(t) x(t) + f(t, x(t))$, $t \in \mathbb T$, where $\mathbb T$ is an invariant under translations time scale and $A \in \mathcal{R}(\mathbb T, \mathbb R^{n \times n})$. We give new criteria ensuring the existence of an asymptotically almost automorphic solution for both equations.

Keywords


Asymptotically almost automorphic functions; nonautonomous equations; exponential dicothomy; ordinary dichotomy

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