Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces

Xiao, Ti‐Jun; Liang, Jin; Zhang, Jun

doi:10.1007/s00233-007-9011-y

Cited by 155 publications

(74 citation statements)

References 4 publications

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“…The concept of pseudo-almost automorphy is a powerful generalization of both the notion of almost automorphy due to Bochner 3 and that of pseudo-almost periodicity due to Zhang see 4 , which has recently been introduced in the literature by Liang et al [5][6][7] . Such a concept, since its introduction in the literature, has recently generated several developments; see, for example, [8][9][10][11][12] .…”

Section: T G T U T a T U T F T U T T ∈ R 12 2 Advances In Diffementioning

confidence: 99%

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Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations

Diagana

2011

Advances in Difference Equations

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Section: T G T U T a T U T F T U T T ∈ R 12 2 Advances In Diffementioning

confidence: 99%

“…Definition 2.6 see Liang et al 5,6 . A function f ∈ BC R, X is called pseudo-almost automorphic if it can be expressed as f g φ, where g ∈ AA X and φ ∈ PAP 0 X .…”

Section: Definition 25mentioning

confidence: 99%

Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations

Diagana

2011

Advances in Difference Equations

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“…More recently, J. Liang et al [17] further developed the theory of the pseudo almost automorphic function, which is more general and complicated than the pseudo almost periodic function and the asymptotically almost automorphic function. One can refer to [16,18,20,32,33,37] for more recent results about the pseudo almost automorphic theory.…”

Section: Introductionmentioning

confidence: 99%

Square-mean pseudo almost automorphic process and its application to stochastic evolution equations

Chen

Lin

2011

Journal of Functional Analysis

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This paper introduces the concept of the square-mean pseudo almost automorphy for a stochastic process. Also it introduces the properties on the completeness and the composition of the space that consists of such processes. With appropriate settings and by virtue of the theory of the semigroups of the operators to an evolution family, the Banach fixed point theorem and the stochastic analysis techniques, this paper investigates the existence, the uniqueness and the global stability of the square-mean pseudo almost automorphic solutions for a general class of stochastic evolution equations. Finally, this paper provides an illustrative example to 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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Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces

Cited by 155 publications

References 4 publications

Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations

Existence of Pseudo-Almost Automorphic Mild Solutions to Some Nonautonomous Partial Evolution Equations

Square-mean pseudo almost automorphic process and its application to stochastic evolution equations

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

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