arXiv subjects
Publications and source records attributed to William Dimbour.
In this paper, we first introduce the concept and properties of {\omega}- periodic limit process. Then we apply specific criteria obtained to investigate asymptotically {\omega}-periodic mild solutions of a Stochastic Differential Equation driven by a Brownian motion. Finally, we give an example to show usefulness of the theoritical results that we obtain in the paper.
In this paper, we make a slight contribution about the existence (uniqueness) and asymptotic stability of the p-th mean S-asymptotically omega-periodic solutions for some nonautonomous Stochastic Evolution Equations driven by a Q-Brownian motion. This is done using the Banach fixed point Theorem and a Gronwall inequality.
In this paper, we show the existence of function which is not S-asymptotically omega-periodic, but which is S-asymptotically omega-periodic in the Stepanov sense. We give sufficient conditions for the existence and uniqueness of S-asymptotically omega-periodic solutions for a nonautonomous differential equation with piecewise constant argument in a Banach space when omega is an integer. This is done using the Banach fixed point Theorem. An example involving the heat operator is discussed as an illustration of the theory.