Weighted pseudo almost periodic functions and applications

Diagana, Toka

doi:10.1016/j.crma.2006.10.008

Cited by 147 publications

(84 citation statements)

References 8 publications

(10 reference statements)

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“…(H5) The space W P AP (X) is translation invariant, that is, the weighted function ρ ∈ U ∞ and satisfies: Remark 3.1. Note that condition (H5) was introduced by Diagana in [5][6][7].…”

Section: Existence Of Weighted Pseudo Almost Periodic Solutionsmentioning

confidence: 99%

“…It is a natural generalization of the classical almost periodicity in the sense of Bochner. Recently, Agarwal and Diagana [4], and Diagana [5][6][7] introduced the concept of weighted pseudo almost periodic functions, which generalizes the one of pseudo almost periodicity. N'Guérékata et al [8] presented stepanov-like almost automorphic functions and discussed its application to monotone differential equations.…”

Section: Introductionmentioning

confidence: 99%

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A new composition theorem for $S^p$-weighted pseudo almost periodic functions and applications to semilinear differential equations

Zhao¹,

Chang²,

N’Guérékata³

2011

OpMath

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Abstract. In this paper, we establish a new composition theorem for S p -weighted pseudo almost periodic functions under weaker conditions than the Lipschitz ones currently encountered in the literatures. We apply this new composition theorem along with the Schauder's fixed point theorem to obtain new existence theorems for weighted pseudo almost periodic mild solutions to a semilinear differential equation in a Banach space.

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“…(H5) The space W P AP (X) is translation invariant, that is, the weighted function ρ ∈ U ∞ and satisfies: Remark 3.1. Note that condition (H5) was introduced by Diagana in [5][6][7].…”

Section: Existence Of Weighted Pseudo Almost Periodic Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new composition theorem for $S^p$-weighted pseudo almost periodic functions and applications to semilinear differential equations

Zhao¹,

Chang²,

N’Guérékata³

2011

OpMath

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“…Generalizations were considered in [11,13,21] and the references therein. In [12], Diagana introduced a new concept which he called weighted pseudo-almost periodicity. The concepts of almost periodicity and pseudo-almost periodicity, and their applications to dynamic equations on time scales are very recent [3,15,27,29].…”

Section: Introductionmentioning

confidence: 99%

Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations

Wang¹,

Agarwal²,

O’Regan³

2017

J. Nonlinear Sci. Appl.

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In this paper, based on the concept and properties of almost-complete closedness time scales (ACCTS), we investigate the existence of weighted pseudo double-almost periodic mild solutions for non-autonomous impulsive evolution equations. We also consider the exponential stability of weighted pseudo double-almost periodic solutions. Finally, we conclude our paper by providing several illustrative applications to different types of dynamic equations and mathematical models. These applications justify the practical usefulness of the established theoretical results.

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“…Then these concepts are generalized in various ways, say, pseudo almost periodicity (Zhang [1][2][3]), weighted pseudo almost periodicity (Diagana [4,5]), pseudo almost automorphy (Liang, Xiao and Zhang [6,7]), weighted pseudo almost automorphy (Blot et al [8]), etc. These concepts have been widely used in the investigation of ordinary differential equations, partial differential equations, functional differential equations and fractional differential equations.…”

Section: Introductionmentioning

confidence: 99%

Translation invariance and related properties of μ-pseudo almost automorphic (periodic) functions with application

2018

Adv Differ Equ

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It is well known that many important properties of μ-pseudo almost automorphic (periodic) functions are based on the translation invariance. In this paper we give a new result of the translation invariance with conditions weaker than the known one. Then some more properties are studied, including the uniqueness of the decomposition and the convolution of the space. Moreover, we present a result on the equality of two spaces of this kind of functions, which extends the well-known results to the case when the measures of the spaces are not equivalent. As an application, we give an existence and uniqueness theorem of μ-pseudo almost automorphic mild solution for a semilinear fractional differential equation.

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Weighted pseudo almost periodic functions and applications

Cited by 147 publications

References 8 publications

A new composition theorem for $S^p$-weighted pseudo almost periodic functions and applications to semilinear differential equations

A new composition theorem for $S^p$-weighted pseudo almost periodic functions and applications to semilinear differential equations

Weighted piecewise pseudo double-almost periodic solution for impulsive evolution equations

Translation invariance and related properties of μ-pseudo almost automorphic (periodic) functions with application

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