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Almost periodic and asymptotically almost periodic functions: part I [PDF]

Advances in Difference Equations, 2018
In this paper, we review indispensable properties and characterizations of almost periodic functions and asymptotically almost periodic functions in Banach spaces.
Dhaou Lassoued, Rahim Shah, Tongxing Li
doaj   +2 more sources

Quasi-Asymptotically Almost Periodic Functions and Applications [PDF]

Bulletin of the Brazilian Mathematical Society, New Series, 2020
The main aim of this paper is to consider the classes of quasi-asymptotically almost periodic functions and Stepanov quasi-asymptotically almost periodic functions in Banach spaces. These classes extend the well known classes of asymptotically almost periodic functions, Stepanov asymptotically almost periodic functions and S-asymptotically ...
Marko Kostic
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Asymptotically Weyl almost periodic functions in Lebesgue spaces with variable exponents [PDF]

Journal of Mathematical Analysis and Applications, 2021
In this paper, we introduce and analyze several different notions of Weyl almost periodic functions and Weyl ergodic components in Lebesgue spaces with variable exponent $L^{p(x)}.$ We investigate the invariance of (asymptotical) Weyl almost periodicity with variable exponent under the actions of convolution products, providing also some illustrative ...
Marko Kostic
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Almost Periodic and Asymptotically Almost Periodic Solutions of Liénard Equations [PDF]

Discrete and Continuous Dynamical Systems - Series B, 2011
The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the Li´enard equation x′′ + f(x)x′ + g(x) = F(t), where F : T !
B. A. Shcherbakov, B. A. Shcherbakov, B. A. Shcherbakov, B. M. Levitan, D. N. Cheban, D. N. Cheban, D. N. Cheban, E. H. Ait Dads, J. Campos, M. Frechet, M. Frechet, P. Cieutat, P. Cieutat, P. Martínez-Amores, T. Caraballo, T. Caraballo, V. V. Zhikov   +16 more
core   +3 more sources

Almost and asymptotically almost periodic solutions of abstract retarded functional difference equations in phase space

Journal of Difference Equations and Applications, 2011
We establish the existence of bounded, almost periodic solutions and asymptotically almost periodic solutions for functional difference equations with infinite delay on abstract phase space. An application to Volterra difference systems with infinite delay is given.
del Campoa, Luis, Pinto Jiménez, Manuel, Vidal, Claudio   +2 more
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New Stability Results for Periodic Solutions of Generalized Van der Pol Oscillator via Second Bogolyubov’s Theorem

Mathematics, 2023
A certain class of nonlinear differential equations representing a generalized Van der Pol oscillator is proposed in which we study the behavior of the existing solution.
Safia Meftah, Fares Yazid, Tefaha Lejdel Ali, Keltoum Bouhali, Abdelkader Moumen, Tariq Alraqad, Hicham Saber   +6 more
doaj   +1 more source

Stepanov-Like Asymptotical Almost Periodic Functions and an Application [PDF]

Journal of Function Spaces, 2018
In this paper, we first study some basic properties of Stepanov-like asymptotical almost periodic functions including the completeness of the space of Stepanov-like asymptotical almost periodic functions. Then, as an application, based on these and the contraction mapping principle, we obtain sufficient conditions for the existence and uniqueness of ...
Yongkun Li, Yaolu Wang, Jianglian Xiang
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Green's functions of and emission into discrete anisotropic and hyperbolic baths

Physical Review Research, 2022
In this paper, we study wave propagation in generic Hermitian local periodic baths and investigate the effects of anisotropy and quasibreaking of periodicity on resonant emission into the band of the bath. We asymptotically decompose the Green's function
Lewis Ruks, Thomas Busch
doaj   +1 more source

Asymptotic Almost Periodic Functions with Range in a Topological Vector Space [PDF]

Journal of Function Spaces and Applications, 2013
The notion of asymptotic almost periodicity was…first introduced by Fréchet in 1941 in the case of…finite dimensional range spaces. Later, its extension to the case of Banach range spaces and locally convex range spaces has been considered by several authors.
Liaqat Ali Khan, Saud M. Alsulami
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Almost periodic and asymptotically almost periodic type functions in Lebesgue spaces with variable exponents Lp(x)

Filomat, 2020
In this paper we introduce and analyze an important class of (asymptotically) Stepanov almost periodic functions in the Lebesgue spaces with variable exponents, which generalizes in a natural fashion all the (asymptotically) almost periodic functions.
Diagana, Toka, Kostić, Marko
openaire   +3 more sources