Stability of unique pseudo almost periodic solutions with measure

Boulbaba Ghanmi; Mohsen Miraoui

Displaying similar documents to “Stability of unique pseudo almost periodic solutions with measure”

New results on stability of periodic solution for CNNs with proportional delays and $D$ operator

Bo Du (2019)

Kybernetika

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The problems related to periodic solutions of cellular neural networks (CNNs) involving $D$ operator and proportional delays are considered. We shall present Topology degree theory and differential inequality technique for obtaining the existence of periodic solution to the considered neural networks. Furthermore, Laypunov functional method is used for studying global asymptotic stability of periodic solutions to the above system.

Characterising weakly almost periodic functionals on the measure algebra

Matthew Daws (2011)

Studia Mathematica

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Let G be a locally compact group, and consider the weakly almost periodic functionals on M(G), the measure algebra of G, denoted by WAP(M(G)). This is a C*-subalgebra of the commutative C*-algebra M(G)*, and so has character space, say $K_{W A P}$ . In this paper, we investigate properties of $K_{W A P}$ . We present a short proof that $K_{W A P}$ can naturally be turned into a semigroup whose product is separately continuous; at the Banach algebra level, this product is simply the natural one induced by the Arens...

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

Marco Kostić, Vipin Kumar (2022)

Archivum Mathematicum

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In this paper, we relate the notions of remote almost periodicity and quasi-asymptotical almost periodicity; in actual fact, we observe that a remotely almost periodic function is nothing else but a bounded, uniformly continuous quasi-asymptotically almost periodic function. We introduce and analyze several new classes of remotely $c$ -almost periodic functions in $ℝ^{n},$ slowly oscillating functions in $ℝ^{n},$ and further analyze the recently introduced class of quasi-asymptotically $c$ -almost periodic...

Fredholmness of pseudo-differential operators with nonregular symbols

Kazushi Yoshitomi (2023)

Czechoslovak Mathematical Journal

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We establish the Fredholmness of a pseudo-differential operator whose symbol is of class $C^{0, σ}$ , $0 < σ < 1$ , in the spatial variable. Our work here refines the work of H. Abels, C. Pfeuffer (2020).

A class of $I_{0}$ -sets

David Grow (1987)

Colloquium Mathematicae

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

M. Kostić (2021)

Archivum Mathematicum

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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...

Existence and uniqueness of periodic solutions for odd-order ordinary differential equations

Yongxiang Li, He Yang (2011)

Annales Polonici Mathematici

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The paper deals with the existence and uniqueness of 2π-periodic solutions for the odd-order ordinary differential equation $u^{(2 n + 1)} = f (t, u, u^{'}, . . ., u^{(2 n)})$ , where $f : ℝ \times ℝ^{2 n + 1} \to ℝ$ is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity $f (t, x ₀, x ₁, . . ., x_{2 n})$ to guarantee the existence and uniqueness are presented. These conditions extend and improve the ones presented by Cong [Appl. Math. Lett. 17 (2004), 727-732].

Positive periodic solutions of a neutral functional differential equation with multiple delays

Yongxiang Li, Ailan Liu (2018)

Mathematica Bohemica

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This paper deals with the existence of positive $ω$ -periodic solutions for the neutral functional differential equation with multiple delays ${(u (t) - c u (t - δ))}^{'} + a (t) u (t) = f (t, u (t - τ_{1}), \dots, u (t - τ_{n})) .$ The essential inequality conditions on the existence of positive periodic solutions are obtained. These inequality conditions concern with the relations of $c$ and the coefficient function $a (t)$ , and the nonlinearity $f (t, x_{1}, \dots, x_{n})$ . Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.

Stable periodic solutions in scalar periodic differential delay equations

Anatoli Ivanov, Sergiy Shelyag (2023)

Archivum Mathematicum

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A class of nonlinear simple form differential delay equations with a $T$ -periodic coefficient and a constant delay $τ > 0$ is considered. It is shown that for an arbitrary value of the period $T > 4 τ - d_{0}$ , for some $d_{0} > 0$ , there is an equation in the class such that it possesses an asymptotically stable $T$ -period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The...

Continuous pseudo-hairy spaces and continuous pseudo-fans

Janusz R. Prajs (2002)

Fundamenta Mathematicae

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A compact metric space X̃ is said to be a continuous pseudo-hairy space over a compact space X ⊂ X̃ provided there exists an open, monotone retraction $r : X ̃ \binom{o n t o}{⟶} X$ such that all fibers $r^{- 1} (x)$ are pseudo-arcs and any continuum in X̃ joining two different fibers of r intersects X. A continuum $Y_{X}$ is called a continuous pseudo-fan of a compactum X if there are a point $c \in Y_{X}$ and a family ℱ of pseudo-arcs such that $⋃ ℱ = Y_{X}$ , any subcontinuum of $Y_{X}$ intersecting two different elements of ℱ contains c, and ℱ is homeomorphic...

Functionals on Banach Algebras with Scattered Spectra

H. S. Mustafayev (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let A be a complex, commutative Banach algebra and let $M_{A}$ be the structure space of A. Assume that there exists a continuous homomorphism h:L¹(G) → A with dense range, where L¹(G) is a group algebra of the locally compact abelian group G. The main results of this note can be summarized as follows: (a) If every weakly almost periodic functional on A with compact spectra is almost periodic, then the space $M_{A}$ is scattered (i.e., $M_{A}$ has no nonempty perfect subset). (b) Weakly almost periodic...

Existence of nonnegative periodic solutions in neutral integro-differential equations with functional delay

Imene Soulahia, Abdelouaheb Ardjouni, Ahcene Djoudi (2015)

Commentationes Mathematicae Universitatis Carolinae

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The fixed point theorem of Krasnoselskii and the concept of large contractions are employed to show the existence of a periodic solution of a nonlinear integro-differential equation with variable delay $x^{'} (t) = - \int_{t - τ (t)}^{t} a (t, s) g (x (s)) d s + \frac{d}{d t} Q (t, x (t - τ (t))) + G (t, x (t), x (t - τ (t))) .$ We transform this equation and then invert it to obtain a sum of two mappings one of which is completely continuous and the other is a large contraction. We choose suitable conditions for $τ$ , $g$ , $a$ , $Q$ and $G$ to show that this sum of mappings fits into the framework of a modification of...

On the uniqueness of periodic decomposition

Viktor Harangi (2011)

Fundamenta Mathematicae

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Let $a ₁, . . ., a_{k}$ be arbitrary nonzero real numbers. An $(a ₁, . . ., a_{k})$ -decomposition of a function f:ℝ → ℝ is a sum $f ₁ + \dots + f_{k} = f$ where $f_{i} : ℝ \to ℝ$ is an $a_{i}$ -periodic function. Such a decomposition is not unique because there are several solutions of the equation $h ₁ + \dots + h_{k} = 0$ with $h_{i} : ℝ \to ℝ a_{i}$ -periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the $(a ₁, . . ., a_{k})$ -decomposition is essentially unique. We characterize those periods for which essential...

A version of the law of large numbers

Katusi Fukuyama (2001)

Colloquium Mathematicae

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By the method of Rio [10], for a locally square integrable periodic function f, we prove $(f (μ ₁^{t} x) + . . . + f (μ ₙ^{t} x)) / n \to \int_{0}^{1} f$ for almost every x and t > 0.

On a question of Demailly-Peternell-Schneider

Meng Chen, Qi Zhang (2013)

Journal of the European Mathematical Society

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We give an affirmative answer to an open question posed by Demailly-Peternell-Schneider in 2001 and recently by Peternell. Let $f : X \to Y$ be a surjective morphism from a log canonical pair $(X, D)$ onto a $ℚ$ -Gorenstein variety $Y$ . If $- (K_{X} + D)$ is nef, we show that $- K_{Y}$ is pseudo-effective.

Three periodic solutions for a class of higher-dimensional functional differential equations with impulses

Yongkun Li, Changzhao Li, Juan Zhang (2010)

Annales Polonici Mathematici

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By using the well-known Leggett–Williams multiple fixed point theorem for cones, some new criteria are established for the existence of three positive periodic solutions for a class of n-dimensional functional differential equations with impulses of the form ⎧y’(t) = A(t)y(t) + g(t,yt), $t \neq t_{j}$ , j ∈ ℤ, ⎨ ⎩ $y (t ⁺_{j}) = y (t ¯_{j}) + I_{j} (y (t_{j}))$ , where $A (t) = {(a_{i j} (t))}_{n \times n}$ is a nonsingular matrix with continuous real-valued entries.

Exponential expressivity of ${ReLU}^{k}$ neural networks on Gevrey classes with point singularities

Joost A. A. Opschoor, Christoph Schwab (2024)

Applications of Mathematics

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We analyze deep Neural Network emulation rates of smooth functions with point singularities in bounded, polytopal domains $D \subset ℝ^{d}$ , $d = 2, 3$ . We prove exponential emulation rates in Sobolev spaces in terms of the number of neurons and in terms of the number of nonzero coefficients for Gevrey-regular solution classes defined in terms of weighted Sobolev scales in $D$ , comprising the countably-normed spaces of I. M. Babuška and B. Q. Guo. As intermediate result, we prove that continuous, piecewise polynomial...

Generalized notions of amenability for a class of matrix algebras

Amir Sahami (2019)

Commentationes Mathematicae Universitatis Carolinae

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We investigate the amenability and its related homological notions for a class of $I \times I$ -upper triangular matrix algebra, say $UP (I, A)$ , where $A$ is a Banach algebra equipped with a nonzero character. We show that $UP (I, A)$ is pseudo-contractible (amenable) if and only if $I$ is singleton and $A$ is pseudo-contractible (amenable), respectively. We also study pseudo-amenability and approximate biprojectivity of $UP (I, A)$ .