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

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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

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

First available in Project Euclid: 14 September 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

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


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.

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