scholarly journals Stepanov-Like Asymptotical Almost Periodic Functions and an Application

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Yongkun Li ◽  
Yaolu Wang ◽  
Jianglian Xiang
Keyword(s):  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Almost Periodic Functions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Delay Differential

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 Stepanov-like asymptotical almost periodic solutions for a class of semilinear delay differential equations.

scholarly journals Almost Periodic Solutions for Second Order Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Wang ◽  
Lan Li
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Time Scales ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Almost Periodic Functions ◽  
Dynamic Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions

We firstly introduce the concept and the properties ofCmalmost periodic functions on time scales, which generalizes the concept of almost periodic functions on time scales and the concept ofC(n)-almost periodic functions. Secondly, we consider the existence and uniqueness of almost periodic solutions for second order dynamic equations on time scales by Schauder’s fixed point theorem and contracting mapping principle. At last, we obtain alternative theorems for second order dynamic equations on time scales.

scholarly journals ALMOST PERIODIC SOLUTIONS OF IMPULSIVE INTEGRO‐DIFFERENTIAL NEURAL NETWORKS

2010 ◽  
Vol 15 (4) ◽  
pp. 505-516 ◽  
Author(s):  
Gani Tr. Stamov ◽  
Jehad O. Alzabut
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Contraction Mapping ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Contraction Mapping Principle ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Cauchy Matrix ◽  
Bellman’S Inequality

In this paper, sufficient conditions are established for the existence of almost periodic solutions for system of impulsive integro‐differential neural networks. Our approach is based on the estimation of the Cauchy matrix of linear impulsive differential equations. We shall employ the contraction mapping principle as well as Gronwall‐Bellman's inequality to prove our main result. The research of Gani Tr. Stamov is partially supported by the Grand 100ni087–16 from Technical University–Sofia

GLOBALLY DYNAMICAL BEHAVIORS FOR DISCRETE LASOTA–WAZEWSKA MODEL WITH SEVERAL DELAYS AND ALMOST PERIODIC COEFFICIENTS

2008 ◽  
Vol 01 (01) ◽  
pp. 95-105 ◽  
Author(s):  
XIAO WANG ◽  
ZHIXIANG LI
Keyword(s):  
Existence And Uniqueness ◽  
Lyapunov Functional ◽  
Contraction Mapping ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Contraction Mapping Principle ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Dynamical Behaviors ◽  
Several Delays

The present paper gives two methods to obtain the existence and uniqueness of almost periodic solution [Formula: see text] of the following discrete Lasota–Wazewska model [Formula: see text] one is a new fixed point theorem in cone proved by us, the other is contraction mapping principle. In addition, some sufficient conditions are established for global attractivity of [Formula: see text] by constructing Lyapunov functional.

Semidirect Product Compactifications

1983 ◽  
Vol 35 (1) ◽  
pp. 1-32
Author(s):  
F. Dangello ◽  
R. Lindahl
Keyword(s):  
Direct Product ◽  
Semidirect Product ◽  
Topological Semigroup ◽  
Sufficient Conditions ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Topological Semigroups ◽  
Weakly Almost Periodic ◽  
Necessary And Sufficient

1. Introduction. K. Deleeuw and I. Glicksberg [4] proved that if S and T are commutative topological semigroups with identity, then the Bochner almost periodic compactification of S × T is the direct product of the Bochner almost periodic compactifications of S and T. In Section 3 we consider the semidirect product of two semi topological semigroups with identity and two unital C*-subalgebras and of W(S) and W(T) respectively, where W(S) is the weakly almost periodic functions on S. We obtain necessary and sufficient conditions and for a semidirect product compactification of to exist such that this compactification is a semi topological semigroup and such that this compactification is a topological semigroup. Moreover, we obtain the largest such compactifications.

scholarly journals Time Remotely Almost Periodic Viscosity Solutions of Hamilton-Jacobi Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Shilin Zhang ◽  
Daxiong Piao
Keyword(s):  
Viscosity Solutions ◽  
Existence And Uniqueness ◽  
Almost Periodic Functions ◽  
Periodic Case ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Jacobi Equations

We study some properties of the remotely almost periodic functions. This paper studies viscosity solutions of general Hamilton-Jacobi equations in the time remotely almost periodic case. Existence and uniqueness results are presented under usual hypotheses.

Hilbert transforms and almost periodic functions

1960 ◽  
Vol 56 (4) ◽  
pp. 354-366 ◽  
Author(s):  
J. Cossar
Keyword(s):  
Hilbert Transform ◽  
Sufficient Conditions ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Hilbert Transforms ◽  
Cauchy Principal ◽  
Principal Value ◽  
Image Position ◽  
The Hilbert Transform

The Hilbert transform, Hf, of a function f is defined by Hf = g, whereP denoting the Cauchy principal value and the integral being assumed to exist in some sense. When f is suitably restricted, Hf exists andIn the first part of Theorem 1 sufficient conditions are given for the validity of (1·2) rather more general than those of Wood ((6), p. 31). The present proof is based on the well-known condition of Riesz for the validity of (1·2), namely, that f is Lp(−∞, ∞) for some p > 1, and on the ‘Parseval’ relation (Lemma 3, (b)), which was used in a similar way by Hardy ((3), p. 110).

scholarly journals Structure of the Set of Bounded Solutions and Existence of Pseudo Almost Periodic Solutions of a Vector Liénard Differential Equation

2019 ◽  
Vol 6 (1) ◽  
pp. 35-56
Author(s):  
◽  
P. Cieutat ◽  
L. Lhachimi
Keyword(s):  
Differential Equation ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Bounded Solutions ◽  
Pseudo Almost Periodic Solution ◽  
Pseudo Almost Periodic Solutions ◽  
Pseudo Almost Periodic

AbstractWe give sufficient conditions ensuring the existence and uniqueness of pseudo almost periodic solution of the vectorial Liénard ’s equation.

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