Almost-periodic quasi-autonomous dissipative systems in a Hilbert space

1981 ◽  
pp. 295-309
Author(s):  
Alain Haraux
Keyword(s):  
Hilbert Space ◽  
Dissipative Systems ◽  
Almost Periodic

Existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay

2019 ◽  
Vol 20 (01) ◽  
pp. 2050003
Author(s):  
Xiao Ma ◽  
Xiao-Bao Shu ◽  
Jianzhong Mao
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Fractional Calculus ◽  
Stochastic Differential Equations ◽  
Periodic Solutions ◽  
Infinite Delay ◽  
Almost Periodic Solutions ◽  
Almost Periodic

In this paper, we investigate the existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay in Hilbert space. The main conclusion is obtained by using fractional calculus, operator semigroup and fixed point theorem. In the end, we give an example to illustrate our main results.

scholarly journals On the Almost Periodic Solutions of Differential Equations on Hilbert Spaces

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Nguyen Thanh Lan
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Hilbert Spaces ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Necessary And Sufficient

For the differential equation , on a Hilbert space , we find the necessary and sufficient conditions that the above-mentioned equation has a unique almost periodic solution. Some applications are also given.

scholarly journals ON THE ENTANGLED ERGODIC THEOREM

2007 ◽  
Vol 10 (01) ◽  
pp. 67-77 ◽  
Author(s):  
FRANCESCO FIDALEO
Keyword(s):  
Hilbert Space ◽  
Ergodic Theorem ◽  
Unitary Operator ◽  
Compact Operators ◽  
Ergodic Average ◽  
Periodic Case ◽  
Almost Periodic ◽  
Ergodic Averages ◽  
Weak Operator Topology ◽  
Weak Operator

Let U be a unitary operator acting on the Hilbert space [Formula: see text], and α: {1, …, m} ↦ {1, …, k} a partition of the set {1, …, m}. We show that the ergodic average [Formula: see text] converges in the weak operator topology if the Aj belong to the algebra of all the compact operators on [Formula: see text]. We write esplicitly the formula for these ergodic averages in the case of pair-partitions. Some results without any restriction on the operators Aj are also presented in the almost periodic case.

Almost Periodic Solutions of Monotone Second-Order Differential Equations

2011 ◽  
Vol 11 (3) ◽  
Author(s):  
Moez Ayachi ◽  
Joël Blot ◽  
Philippe Cieutat
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Periodic Solution ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Second Order Differential Equations

AbstractWe give sufficient conditions for the existence of almost periodic solutions of the secondorder differential equationu′′(t) = f (u(t)) + e(t)on a Hilbert space H, where the vector field f : H → H is monotone, continuous and the forcing term e : ℝ → H is almost periodic. Notably, we state a result of existence and uniqueness of the Besicovitch almost periodic solution, then we approximate this solution by a sequence of Bohr almost periodic solutions.

scholarly journals Cloud Service for Numerical Calculations and Visualizations of Photonic Dissipative Systems

2017 ◽  
Vol 17 (5) ◽  
pp. 89-100
Author(s):  
Hayk Grigoryan ◽  
Hrachya Astsatryan ◽  
Tigran Gevorgyan ◽  
Vahe Manukyan
Keyword(s):  
Hilbert Space ◽  
Density Matrix ◽  
Time Evolution ◽  
Quantum Physics ◽  
Open Systems ◽  
Cloud Service ◽  
Quantum Systems ◽  
Distribution Functions ◽  
Numerical Calculations ◽  
Dissipative Systems

Abstract Nowadays quantum physics is crucial for several scientific applications, where it is no longer possible to neglect the environmental interaction, like dissipation and decoherence. In these cases, the quantum systems are usually treated as open systems and their time-evolution is described by a density matrix in frames of the master equation, instead of the Hilbert-space vector and the Schrodinger equation. The visualization of such quantum systems allows users to calculate and study the sensitivity of the parameters, like excitation photon numbers or photonnumber distribution functions or Wigner functions. In this paper, a cloud service for numerical calculations and visualization of photonic dissipative systems is presented, which enables numerical simulations and visualizations of a wide variety of Hamiltonians, including those with arbitrary time-dependences widely used in many physics applications. The service allows creating graphics and charts for interacting complex systems and simulating their time evolution with many available timeevolution drivers.

scholarly journals Convexity, boundedness, and almost periodicity for differential equations in Hillbert space

1979 ◽  
Vol 2 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Jerome A. Goldstein
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Bounded Solution ◽  
Normal Operator ◽  
Sufficient Condition ◽  
Differential Inequalities ◽  
Almost Periodic ◽  
Bounded Solutions ◽  
General Sufficient Condition ◽  
Convexity Inequality

There are three kinds of results. First we extend and sharpen a convexity inequality of Agmon and Nirenberg for certain differential inequalities in Hilbert space. Next we characterize the bounded solutions of a differential equation in Hilbert space involving and arbitrary unbounded normal operator. Finally, we give a general sufficient condition for a bounded solution of a differential equation in Hilbert space to be almost periodic.

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