Composition of pseudo almost periodic and pseudo almost automorphic functions and applications to evolution equations

Cieutat, Philippe; Fatajou, Samir; N’Guérékata, Gaston M.

doi:10.1080/00036810903397503

Cited by 46 publications

(19 citation statements)

References 11 publications

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“…Remark 2.2. Notice in particular that if f 1 satisfies the Lipschitz condition stated above and f 1 (t, x) is almost periodic on R for all x ∈ X, then f 1 is almost periodic uniformly for x ∈ X ranging over compact subsets of X (see [6,Lemma 2.6] and [4, Theorem 3.12]), which means that the Lipschitz condition of Definition 2.1 for f 1 would work to reduce the almost periodic property of f 1 to simply asking for f 1 (t, x) being almost periodic on R for all x ∈ X.…”

Section: Resultsmentioning

confidence: 99%

Asymptotic Almost Periodicity to Some Evolution Equations

Wang¹,

Xiang²,

Zhou³

2015

Z. Anal. Anwend.

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In this paper, we introduce a new notion of semi-Lipschitz continuity for the class of asymptotically almost periodic functions and establish new existence theorems for asymptotically almost periodic mild solutions to some semilinear abstract evolution equations upon making some suitable assumptions. As one would expect, the results presented here would generalize and improve some recent results in this area.

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Section: Resultsmentioning

confidence: 99%

Asymptotic Almost Periodicity to Some Evolution Equations

Wang¹,

Xiang²,

Zhou³

2015

Z. Anal. Anwend.

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“…We have a similar characterization for almost periodic functions: f ∈ AP u (R × X, X) if and only if ∀x ∈ X, t → f (t, x) ∈ AP(R, X) and f is uniformly continuous on each compact K of X with respect to t (see [17,Lemma 2.6]). …”

Section: Remark 22mentioning

confidence: 92%

Almost automorphic solutions for some evolution equations through the minimizing for some subvariant functional, applications to heat and wave equations with nonlinearities

Cieutat

Ezzinbi²

2011

Journal of Functional Analysis

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In this work, we study the existence of bounded and almost automorphic solutions for evolution equations in Banach spaces. We suppose that the linear part is the infinitesimal generator of a compact C 0 -semigroup of bounded linear operators and the nonlinear part is an almost automorphic function with respect to the second argument. We give sufficient conditions ensuring the existence of an almost automorphic solution when there is at least one bounded solution on R + . We use the subvariant functional method to show that every K-minimizing mild solution is compact almost automorphic. Applications are provided for both heat and wave equations with nonlinearities in several functional spaces.

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“…However, this fact is true in a uniformly convex Banach space V and hence in every Hilbert space, see Theorem 2.1. In the second place we need a composition result [7], which will be fundamental for the analysis of (1.4) and (1.1), see Proposition 2.2. Proposition 2.2.…”

Section: 2mentioning

confidence: 99%

Almost automorphic delayed differential equations and Lasota-Wazewska model

Coronel¹,

Maulén²,

Pinto³

et al. 2017

Discrete &Amp; Continuous Dynamical Systems - A

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Existence of almost automorphic solutions for abstract delayed differential equations is established. Using ergodicity, exponential dichotomy and Bi-almost automorphicity on the homogeneous part, sufficient conditions for the existence and uniqueness of almost automorphic solutions are given.Date: August 1, 2018. Key words and phrases. Abstract delay differential equations, Almost automorphic, Exponential dichotomy, Ergodicity, Evolution operator.

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Composition of pseudo almost periodic and pseudo almost automorphic functions and applications to evolution equations

Cited by 46 publications

References 11 publications

Asymptotic Almost Periodicity to Some Evolution Equations

Asymptotic Almost Periodicity to Some Evolution Equations

Almost automorphic solutions for some evolution equations through the minimizing for some subvariant functional, applications to heat and wave equations with nonlinearities

Almost automorphic delayed differential equations and Lasota-Wazewska model

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