Almost automorphic solutions of nonautonomous evolution equations

Ding, Hui-Sheng; Wei, Long; N’Guérékata, Gaston M.

doi:10.1016/j.na.2008.09.005

Cited by 19 publications

(13 citation statements)

References 29 publications

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“…About the existence of almost automorphic mild solution of (1.3) when (A(t)) t∈R+ is exponentially stable and when f ∈ AAU(R+ × X, X) we can see [5].…”

Section: Remark 54mentioning

confidence: 99%

Local attractivity in nonautonomous semilinear evolution equations

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Buşe

Cieutat

2014

Nonautonomous Dynamical Systems

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We study the local attractivity of mild solutions of equations in the formwhere A(t) are (possible) unbounded linear operators in a Banach space and where f is a (possible) nonlinear mapping. Under conditions of exponential stability of the linear part, we establish the local attractivity of various kinds of mild solutions. To obtain these results we provide several results on the Nemytskii operators on the space of the functions which converge to zero at in nity.

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“…About the existence of almost automorphic mild solution of (1.3) when (A(t)) t∈R+ is exponentially stable and when f ∈ AAU(R+ × X, X) we can see [5].…”

Section: Remark 54mentioning

confidence: 99%

Local attractivity in nonautonomous semilinear evolution equations

Blot

Buşe

Cieutat

2014

Nonautonomous Dynamical Systems

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“…They were introduced by Bochner [1,2]; for more details about this topic, we refer the reader to [3,4]. In recent years, the existence of almost periodic and almost automorphic solutions on different kinds of deterministic differential equations have been considerably investigated in lots of publications [5][6][7][8][9][10][11][12][13][14][15] because of its significance and applications in physics, mechanics, and mathematical biology.…”

Section: D[x(t) − F T B 1 X(t) ] = [Ax(t) + G(t B 2 X(t))]dt + H(tmentioning

confidence: 99%

Square-mean almost automorphic mild solutions to some stochastic differential equations in a Hilbert space

2011

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This article deals primarily with the existence and uniqueness of square-mean almost automorphic mild solutions for a class of stochastic differential equations in a real separable Hilbert space. We study also some properties of square-mean almost automorphic functions including a compostion theorem. To establish our main results, we use the Banach contraction mapping principle and the techniques of fractional powers of an operator. Mathematics Subject Classification (2000) 34K14, 60H10, 35B15, 34F05.

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“…It was named as PAA functions because they originally presented themselves, in their work in differential geometry, as scalars and tensors on manifolds with (discrete) groups of automorphisms [3]. Later, PKK function has become one of the most attractive topics in the qualitative theory of evolution equations, and there have been several interesting, natural and powerful generalizations of the classical PKK functions [4][5][6][7][8][9]. Recently, Digana et al, studied the concept for different classes of ODF and PDE (see [10][11][12][13][14]).…”

Section: Introductionmentioning

confidence: 99%

Symmetric-periodic solutions for some types of generalized neutral equations

2016

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The existence of symmetric-periodic outcomes for a class of fractional differential equations has been increasingly studied. Such study has used various methods such as fixed point theory, critical point theory, and approximation theory. In this work, we study the m-pseudo almost automorphic (m-PKK) outcomes for a category of fractional neutral differential equations. To satisfy this aim, we introduce composition results under suitable conditions and employ them to establish some extant outcomes using interpolation theory mixed with fixed point technique. Examples are illustrated.

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Almost automorphic solutions of nonautonomous evolution equations

Cited by 19 publications

References 29 publications

Local attractivity in nonautonomous semilinear evolution equations

Local attractivity in nonautonomous semilinear evolution equations

Square-mean almost automorphic mild solutions to some stochastic differential equations in a Hilbert space

Symmetric-periodic solutions for some types of generalized neutral equations

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