Jaqueline G. Mesquita

A connection between almost periodic functions defined on timescales and ℝ

In this paper, we prove a strong connection between almost periodic functions on timescales and almost periodic functions on . An application to difference equations on is given.

Continuous dependence for impulsive functional dynamic equations involving variable time scales

Using a known correspondence between the solutions of impulsive measure functional differential equations and the solutions of impulsive functional dynamic equations on time scales, we prove that the limit of solutions of impulsive functional dynamic equations over a convergent sequence of time scales converges to a solution of an impulsive functional dynamic equation over the limiting time scale.

Global Mild Solutions for a Nonautonomous 2D Navier–Stokes Equations with Impulses at Variable Times

The present paper deals with existence and uniqueness of global mild solutions for a new model of Navier–Stokes equations on

Measure functional differential equations and functional dynamic equations on time scales

\mathbb {R}^2

Almost automorphic solutions of non-autonomous difference equations

R2 subjected to impulse effects at variable times. By using the framework of impulsive/nonautonomous dynamical systems we are able to consider impulse effects in the system as well relax conditions on the external forcing term which is, in our case, non-linear and explicitly time-dependent, extending previous results on the specialized literature. Moreover, we also introduce sufficient conditions on the structure of the impulse set which ensure dissipativity for the system, i.e., uniform boundedness of global solutions starting in bounded sets, which is an indicative to the existence of objects as attractors.