Almost Periodic Solutions of the Differential Equation in Locally Convex Spaces

2021 ◽  
pp. 125-128
Author(s):  
Gaston M. N’Guérékata
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Locally Convex Spaces ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Locally Convex ◽  
Convex Spaces

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 Study Of Asymptotically Almost Periodic Solutions of a Class of Impulsive Population Models

2018 ◽  
Vol 36 (3) ◽  
pp. 597-601
Author(s):  
Li Wang
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Population Models ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Laplacian Equation ◽  
Existence Of Periodic Solutions ◽  
Functional Differential ◽  
Solutions Of Equations ◽  
Asymptotically Almost Periodic

Based on the Mawhin continuous theorem, the existence of strictly positive asymptotically almost periodic solutions of a class of impulsive population models is studied. The conclusion generalizes the conclusion of the existing literatures. Since the Mawhin continuous theorem is only used to prove the existence of periodic solutions or almost periodic solutions of equations (for example:impulsive differential equation, functional differential equation, integral equation, Lienard equation, P-Laplacian equation), the main result is innovative.

scholarly journals The frequencies of almost periodic solutions of almost periodic differential equations

1974 ◽  
Vol 17 (3) ◽  
pp. 332-344
Author(s):  
G. C. O'Brien
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
First Order ◽  
Periodic Differential Equation ◽  
Right Hand

AbstractAlmost periodic solutions of a first order almost periodic differential equation in Rp are shown to have less than p basic frequencies additional to the basic frequencies of the almost periodic right hand of the equation.

STABILITY AND MULTIPLICITY OF PERIODIC OR ALMOST PERIODIC SOLUTIONS TO SCALAR FIRST-ORDER ODE

2006 ◽  
Vol 04 (03) ◽  
pp. 237-246 ◽  
Author(s):  
ALAIN HARAUX
Keyword(s):  
Differential Equation ◽  
Periodic Solutions ◽  
Monotonicity Property ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
First Order ◽  
Autonomous Equation ◽  
Stability Pattern ◽  
The Stability ◽  
Scalar Differential Equation

Using a monotonicity property specific to this case, we give a general property of the stability pattern of successive periodic solutions of the first-order scalar differential equation u′ = f(t, u). We also give an optimal smallness condition in order for the quasi-autonomous equation u′+g(u) = f(t) where g ∈ C1(ℝ) and f : ℝ → ℝ is almost periodic to have exactly N almost periodic solutions on the line assuming that we have exactly N equilibria ci and g′(ci) ≠ 0 for all i.

scholarly journals On a functional differential equation in locally convex spaces

1983 ◽  
Vol 27 (2) ◽  
pp. 269-283
Author(s):  
Sadayuki Yamamuro
Keyword(s):  
Differential Equation ◽  
Functional Differential Equation ◽  
Convex Space ◽  
Locally Convex Space ◽  
Locally Convex Spaces ◽  
Functional Differential ◽  
Nonlinear Maps ◽  
Locally Convex ◽  
Convex Spaces

The notion of accretiveness for multi-valued nonlinear maps is defined in locally convex spaces and it is used to obtain a locally convex space version of a result of M.G. Crandall and J.A. Nohel.

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