Pseudo almost periodic solutions of infinite class under the light of measure theory and applications
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DOI: 10.1002/mma.7051
Abstract: The aim of this work is to present a new approach to study weighted pseudo almost periodic functions with infinite delay using the measure theory. We study the existence and uniqueness of (μ, ν)‐pseudo almost periodic… read more here.
Keywords: periodic solutions; solutions infinite; infinite class; almost periodic ... See more keywords
Periodic and Almost Periodic Solutions for a Coupled System of Two Korteweg-de Vries Equations with Boundary Forces
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DOI: 10.1007/s00009-018-1191-z
Abstract: In this paper, we investigate a coupled system of two Korteweg-de Vries equations on a bounded domain. We discuss the long-time behavior of this system with forces on the left Dirichlet boundary conditions. We obtain… read more here.
Keywords: periodic almost; system; system two; almost periodic ... See more keywords
Perturbation Theory for Almost-Periodic Potentials I: One-Dimensional Case
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DOI: 10.1007/s00220-019-03329-3
Abstract: We consider the family of operators $${H^{(\varepsilon)}:=-\frac{d^2}{dx^2}+\varepsilon V}$$H(ε):=-d2dx2+εV in $${\mathbb{R}}$$R with almost-periodic potential V. We study the behaviour of the integrated density of states (IDS) $${N(H^{(\varepsilon)};\lambda)}$$N(H(ε);λ) when $${\varepsilon\to 0}$$ε→0 and $${\lambda}$$λ is a fixed energy.… read more here.
Keywords: theory almost; varepsilon; perturbation theory; almost periodic ... See more keywords
Polyhedral Billiards, Eigenfunction Concentration and Almost Periodic Control
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DOI: 10.1007/s00220-020-03741-0
Abstract: We study dynamical properties of the billiard flow on convex polyhedra away from a neighbourhood of the non-smooth part of the boundary, called “pockets”. We prove there are only finitely many immersed periodic tubes missing… read more here.
Keywords: control; almost periodic; polyhedral billiards; concentration ... See more keywords
Persistence of Invariant Tori in Integrable Hamiltonian Systems Under Almost Periodic Perturbations
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DOI: 10.1007/s00332-018-9467-9
Abstract: In this paper, we are concerned with the existence of invariant tori in nearly integrable Hamiltonian systems $$\begin{aligned} H=h(y)+f(x,y,t), \end{aligned}$$H=h(y)+f(x,y,t),where $$y\in D\subseteq \mathbb {R}^n$$y∈D⊆Rn with D being an open bounded domain, $$x\in \mathbb {T}^n$$x∈Tn, f(x, y, t)… read more here.
Keywords: persistence invariant; almost periodic; mathbb; hamiltonian systems ... See more keywords
On almost periodic processes in impulsive fractional-order competitive systems
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DOI: 10.1007/s10910-017-0805-1
Abstract: In this paper an impulsive model for the dynamics of competitive Lotka–Volterra systems using the Caputo fractional-order derivative is developed. The existence and uniqueness of almost periodic solutions are investigated. Applying the fractional Lyapunov method,… read more here.
Keywords: competitive systems; fractional order; almost periodic; periodic processes ... See more keywords
Almost Periodic Solutions of Functional Equations
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DOI: 10.1007/s10958-017-3305-8
Abstract: We establish conditions for the existence of almost periodic solutions of linear and nonlinear almost periodic functional equations without using the -classes of these equations. read more here.
Keywords: almost periodic; functional equations; periodic solutions; solutions functional ... See more keywords
Pseudo-Almost Periodic Solution on Time-Space Scales for a Novel Class of Competitive Neutral-Type Neural Networks with Mixed Time-Varying Delays and Leakage Delays
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DOI: 10.1007/s11063-017-9620-8
Abstract: A competitive neural network model was proposed to describe the dynamics of cortical maps in which, there exist two memories: long-term and short-term. In this paper, we investigate the existence and the exponential stability of… read more here.
Keywords: periodic solution; time space; time; almost periodic ... See more keywords
Exponential Stability of Pseudo Almost Periodic Solutions for Fuzzy Cellular Neural Networks with Time-Varying Delays
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DOI: 10.1007/s11063-018-9857-x
Abstract: This paper considers the exponential stability of pseudo almost periodic solutions for a class of fuzzy cellular neural networks with time-varying delays. Based on differential inequality techniques and by constructing suitable Lyapunov function, we achieve… read more here.
Keywords: stability pseudo; periodic solutions; almost periodic; pseudo almost ... See more keywords
Almost Periodic Solutions for Systems with Delay and Nonfixed Times of Impulsive Actions
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DOI: 10.1007/s11253-017-1320-z
Abstract: We study the existence and asymptotic stability of piecewise continuous almost periodic solutions for systems of differential equations with delay and nonfixed times of impulsive actions that can be regarded as mathematical models of neural… read more here.
Keywords: periodic solutions; solutions systems; delay nonfixed; times impulsive ... See more keywords
Favard–Amerio Theory for Almost Periodic Functional-Differential Equations Without Using the ℋ-Classes of These Equations
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DOI: 10.1007/s11253-017-1404-9
Abstract: The Favard–Amerio theory is constructed for almost periodic functional-differential equations in Banach spaces without using the ℋ-classes of these equations. For linear equations, we present the first example of an almost periodic operator, which has… read more here.
Keywords: almost periodic; periodic functional; amerio theory; favard amerio ... See more keywords