By using the roughness theory of exponential dichotomies and the contraction mapping, some sufficient conditions are obtained for the existence and uniqueness of pseudo almost periodic solution of the above differential equation with piecewise constant argument
The main goal of the paper concerns two parts, in the ˝rst one, we extend some results from Blot et al [5] under general hypothesis on the measure, in the second part, we introduce a new class of functions, which we call measure pseudo 𝒮 - asymptotically omega periodic functions. The obtained results is the extension of those established recently in the literature. Then we establish many interesting results on those functions, namely their characterization, we give also several properties of those class of functions as composition results, the invariance by translation, and the convolution product. All sections are illustrated by examples or counter examples.
We give sufficient conditions ensuring the existence and uniqueness of an Eberlein-weakly almost periodic solution to the following linear equationin a Banach space X, where is a family of infinitesimal generators such that for all ,for some for which the homogeneuous linear equationA t x t t is well posed, stable and has an exponential dichotomy, and :is Eberlein-weakly amost periodic.
In this work, we study the existence and uniqueness of pseudo almost periodic solutions for some difference equations. Firstly, we investigate the spectrum of the shift operator on the space of pseudo almost periodic sequences to show the main results of this work. For the illustration, some applications are provided for a second order differential equation with piecewise constant arguments.
We study the response of various linear and nonlinear differential equations to different kinds of forced oscillations, specially the periodic and almost periodic oscillations. A special attention is given to differential equations with time-almost periodic type and state-dependent delays. To the best of our knowledge, there are no results in literature that address this problem.
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