On the Bohr transform of almost‐periodic solutions for some differential equations in abstract spaces

Zaidman, S.

doi:10.1155/s0161171201012352

Cited by 2 publications

(1 citation statement)

References 7 publications

(5 reference statements)

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“…In [15] and [22], the authors studied the existence and uniqueness, attractiveness for a pseudo almost periodic automorphic solution for some general dissipative systems in Banach spaces. Let us indicate the contribution of Zaidman on almost periodic and automorphic functions (see for instance [46][47][48][49]). Fink introduced in the literature the concept of subvariant functional in [25] to prove the existence of compact almost automorphic solutions for the following ordinary differential equation…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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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Massera Type Theorems for Abstract Functional Differential Equations

Liu

Minh

N’Guérékata

et al. 2008

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Abstract. The paper is concerned with conditions for the existence of almost periodic solutions of the following abstract functional di¤erential equation _ u uðtÞ ¼ AuðtÞ þ ½BuðtÞ þ f ðtÞ; where A is a closed operator in a Banach space X, B is a general bounded linear operator in the function space of all X-valued bounded and uniformly continuous functions that satisfies a so-called autonomous condition. We develop a general procedure to carry out the decomposition that does not need the wellposedness of the equations. The obtained conditions are of Massera type, which are stated in terms of spectral conditions of the operator A þ B and the spectrum of f . Moreover, we give conditions for the equation not to have quasi-periodic solutions with di¤erent structures of spectrum. The obtained results extend previous ones.

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On the Bohr transform of almost‐periodic solutions for some differential equations in abstract spaces

Abstract: Abstract. We consider abstract differential equations of the formwe establish connections between their Bohr-transforms,û(λ) andf (λ).

Cited by 2 publications

References 7 publications

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

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

Massera Type Theorems for Abstract Functional Differential Equations

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