African Diaspora Journal of Mathematics

Pseudo-Almost Periodic and Pseudo-Almost Automorphic Solutions of Class r Under the Light of Measure Theory

Issa Zabsonre and Hamidou Toure

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The aim of this work is to present new approach to study weighted pseudo almost periodic and automorphic functions using the measure theory. We present a new concept of weighted ergodic functions which is more general than the classical one. Then we establish many interesting results on the functional space of such functions. We study the existence and uniqueness of $(\mu,\nu)$-pseudo almost periodic and automorphic solutions of class $r$ for some neutral partial functional differential equations in a Banach space when the delay is distributed using the spectral decomposition of the phase space developed in Adimy and co-authors. Here we assume that the undelayed part is not necessarily densely defined and satisfies the well-known Hille-Yosida condition, the delayed part are assumed to be pseudo almost periodic with respect to the first argument and Lipschitz continuous with respect to the second argument.

Article information

Source
Afr. Diaspora J. Math. (N.S.), Volume 19, Number 1 (2016), 58-86.

Dates
First available in Project Euclid: 14 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.adjm/1473854198

Mathematical Reviews number (MathSciNet)
MR3538976

Zentralblatt MATH identifier
1356.34077

Subjects
Primary: 34K14: Almost and pseudo-periodic solutions 34K30: Equations in abstract spaces [See also 34Gxx, 35R09, 35R10, 47Jxx] 35B15: Almost and pseudo-almost periodic solutions 35K57: Reaction-diffusion equations 44A35: Convolution 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]

Keywords
measure theory ergodicity $(\mu,\nu)$-pseudo almost periodic function evolution equations reaction diffusion system partial functional differential equations

Citation

Zabsonre, Issa; Toure, Hamidou. Pseudo-Almost Periodic and Pseudo-Almost Automorphic Solutions of Class r Under the Light of Measure Theory. Afr. Diaspora J. Math. (N.S.) 19 (2016), no. 1, 58--86. https://projecteuclid.org/euclid.adjm/1473854198


Export citation