Ergodicity and asymptotically almost periodic solutions of some differential equations

Zhang, Chuanyi

doi:10.1155/s016117120100429x

Cited by 9 publications

(11 citation statements)

References 16 publications

(20 reference statements)

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“…Proof. Due to (i)-(ii) and Lemma 2.1, we get that for each x ∈ AAP (I : X) one has f (·, x(·)) ∈ AAP S q (I : X), where q = pr/p + r; here we would like to recall only that the range of an X-valued asymptotically almost periodic function is relatively compact in X by [32,Theorem 2.4]. Owing to the assumption (iii), Lemma 2.7 and the obvious equality lim t→+∞ S γ (t)x 0 = 0, we get that the mapping Υ : AAP (X) → AAP (X) is well-defined.…”

Section: Asymptotically Almost Periodic Solutions Of Abstract Fractionalmentioning

confidence: 97%

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Asymptotically almost periodic solutions of fractional relaxation inclusions with Caputo derivatives

Kostić¹

2018

Publ Inst Math (Belgr)

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In the paper under review, we analyze asymptotically almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. As auxiliary tools, we use subordination principles, fixed point theorems and the well known results on the generation of infinitely differentiable degenerate semigroups with removable singularites at zero. Our results are well illustrated and seem to be not considered elsewhere even for fractional relaxation equations with almost sectorial operators.2010 Mathematics Subject Classification. 34G25, 47D03, 47D06, 47D99. Key words and phrases. Abstract semilinear Cauchy inclusions, Asymptotic almost periodicity, Stepanov asymptotic almost periodicity.

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Section: Asymptotically Almost Periodic Solutions Of Abstract Fractionalmentioning

confidence: 97%

“…Concerning almost periodic and asymptotically almost periodic solutions of various classes of abstract Volterra integro-differential equations in Banach spaces, the reader may consult [1], [4]- [5], [9]- [11], [18]- [25] and [32].…”

Section: Introductionmentioning

confidence: 99%

Asymptotically almost periodic solutions of fractional relaxation inclusions with Caputo derivatives

Kostić¹

2018

Publ Inst Math (Belgr)

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“…By AP (I : E) we denote the vector space consisting of all almost periodic functions from the interval I into E. Equipped with the sup-norm, AP (I : E) becomes a Banach space. The function f : I → E is said to be asymptotically almost periodic iff there exist an almost periodic function h : I → E and a function φ ∈ C 0 (I : E) such that f (t) = h(t) + φ(t) for all t ∈ I (the existing literature is somewhat controversial about the definition of an asymptotically almost periodic f : R → E; in the case that I = R, we will use here the approach of C. Zhang from [41]). This is equivalent to saying that, for every > 0, we can find numbers l > 0 and M > 0 such that every subinterval of I of length l contains, at least, one number τ such that f (t + τ ) − f (t) ≤ provided |t|, |t + τ | ≥ M.…”

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confidence: 99%

Almost periodic type functions and densities

Kostić¹

2022

EECT

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In this paper, we introduce and analyze the notions of g-almost periodicity and Stepanov g-almost periodicity for functions with values in complex Banach spaces. In order to do that, we use the recently introduced notions of lower and upper (Banach) g-densities. We also analyze uniformly recurrent functions, generalized almost automorphic functions and apply our results in the qualitative analysis of solutions of inhomogeneous abstract integrodifferential inclusions. We present plenty of illustrative examples, results of independent interest, questions and unsolved problems.

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“…For the purpose of research of (asymptotically) almost periodic properties of solutions to semilinear Cauchy inclusions, we need to remind ourselves of the following well-known definitions and results (see, e.g., Zhang [34], Long and Ding [35] and Proposition 2.6 below). The following composition principles are well known in the existing literature (see, e.g., [34]).…”

Section: Asymptotically Almost Periodic Functionsmentioning

confidence: 99%

Almost periodic and asymptotically almost periodic functions: part I

Lassoued

Shah

2018

Adv Differ Equ

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In this paper, we review indispensable properties and characterizations of almost periodic functions and asymptotically almost periodic functions in Banach spaces. Special accent is put on the Stepanov generalizations of almost periodic functions and asymptotically almost periodic functions. We also recollect some basic results regarding equi-Weyl-almost periodic functions and Weyl-almost periodic functions. The class of asymptotically Weyl-almost periodic functions, introduced in this work, seems to be not considered elsewhere even in the scalar-valued case. We actually introduce eight new classes of asymptotically almost periodic functions and analyze relations between them. In order to make a picture as complete and clear as possible, several illustrating examples and counter-examples are given. It is worth noting that the topics dealt with in this paper seem to be of an intrinsic connection with the problem of existence and uniqueness of solutions of differential and difference equations, in both determinist and stochastic cases. MSC: 42A75

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Ergodicity and asymptotically almost periodic solutions of some differential equations

Cited by 9 publications

References 16 publications

Asymptotically almost periodic solutions of fractional relaxation inclusions with Caputo derivatives

Asymptotically almost periodic solutions of fractional relaxation inclusions with Caputo derivatives

Almost periodic type functions and densities

Almost periodic and asymptotically almost periodic functions: part I

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