Partially irregular almost periodic solutions of ordinary differential systems

Alexandr Demenchuk

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Some problems concerning different types of vector valued almost periodic functions

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CONTENTS Introduction.............................................................51. Notation, preliminaries, main definitions and solution of problem (D)...................6 1.1. Notation............................................................6 1.2. Preliminaries.......................................................7 1.3. Main definitions....................................................8 1.4. Problem (D).........................................................82....

Approximation of almost periodic functions by periodic ones

Alexander Fischer (1998)

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It is not the purpose of this paper to construct approximations but to establish a class of almost periodic functions which can be approximated, with an arbitrarily prescribed accuracy, by continuous periodic functions uniformly on $ℝ = (- \infty; + \infty)$ .

Periodic Solutions of Periodic Retarded Functional Differential Equations

Marcin Pawłowski (2004)

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The paper presents a geometric method of finding periodic solutions of retarded functional differential equations (RFDE) $x^{'} (t) = f (t, x_{t})$ , where f is T-periodic in t. We construct a pair of subsets of ℝ × ℝⁿ called a T-periodic block and compute its Lefschetz number. If it is nonzero, then there exists a T-periodic solution.

Existence and uniqueness of positive periodic solutions for a class of integral equations with parameters

Shu-Gui Kang, Bao Shi, Sui Sun Cheng (2009)

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Existence of periodic solutions of functional differential equations with parameters such as Nicholson’s blowflies model call for the investigation of integral equations with parameters defined over spaces with periodic structures. In this paper, we study one such equation $ϕ (x) = λ \int_{[x, x + ω] \cap Ω} K (x, y) h (y) f (y, ϕ (y - τ (y))) d y$ , x ∈ Ω, by means of the proper value theory of operators in Banach spaces with cones. Existence, uniqueness and continuous dependence of proper solutions are established.

On Riemann integrability and almost periodic functions

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Generalized $c$ -almost periodic type functions in $ℝ^{n}$

M. Kostić (2021)

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In this paper, we analyze multi-dimensional quasi-asymptotically $c$ -almost periodic functions and their Stepanov generalizations as well as multi-dimensional Weyl $c$ -almost periodic type functions. We also analyze several important subclasses of the class of multi-dimensional quasi-asymptotically $c$ -almost periodic functions and reconsider the notion of semi- $c$ -periodicity in the multi-dimensional setting, working in the general framework of Lebesgue spaces with variable exponent. We provide...

New spectral criteria for almost periodic solutions of evolution equations

Toshiki Naito, Nguyen Van Minh, Jong Son Shin (2001)

Studia Mathematica

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We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where $\bar{e^{i s p (f)}}$ may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*)...

Periodic solutions of evolution problem associated with moving convex sets

Charles Castaing, Manuel D.P. Monteiro Marques (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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This paper is concerned with periodic solutions for perturbations of the sweeping process introduced by J.J. Moreau in 1971. The perturbed equation has the form $- D u \in N_{C (t)} (u (t)) + f (t, u (t))$ where C is a T-periodic multifunction from [0,T] into the set of nonempty convex weakly compact subsets of a separable Hilbert space H, $N_{C (t)} (u (t))$ is the normal cone of C(t) at u(t), f:[0,T] × H∪H is a Carathéodory function and Du is the differential measure of the periodic BV solution u. Several existence results of periodic solutions...