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.

An Existence Result for Stepanoff Almost-Periodic Differential Equations

1971 ◽  
Vol 14 (4) ◽  
pp. 551-554 ◽  
Author(s):  
S. Zaidman
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Hilbert Spaces ◽  
Existence Result ◽  
Order Differential Equation ◽  
Short Paper ◽  
Almost Periodic ◽  
First Order ◽  
Right Hand

In this short paper we present an existence (an unicity) result for a first order differential equation in Hilbert spaces with right-hand side almost-periodic in the sense of Stepanoff.

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 Almost Periodic Solutions of First-Order Ordinary Differential Equations

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 171 ◽  
Author(s):  
Seifedine Kadry ◽  
Gennady Alferov ◽  
Gennady Ivanov ◽  
Artem Sharlay
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Upper And Lower Bounds ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
First Order ◽  
Existence And Stability ◽  
Solutions Of Equations ◽  
The Right

Approaches to estimate the number of almost periodic solutions of ordinary differential equations are considered. Conditions that allow determination for both upper and lower bounds for these solutions are found. The existence and stability of almost periodic problems are studied. The novelty of this paper lies in the fact that the use of apparatus derivatives allows for the reduction of restrictions on the degree of smoothness of the right parts. In the works of Lebedeva [1], regarding the number of periodic solutions of equations first order, they required a high degree of smoothness. Franco et al. required the smoothness of the second derivative of the Schwartz equation [2]. We have all of these restrictions lifted. Our new form presented also emphasizes this novelty.

Existence of almost periodic solutions of stochastic differential equations with periodic coefficients

2017 ◽  
Vol 25 (1) ◽  
Author(s):  
Mohamed-Ahmed Boudref ◽  
Ahmed Berboucha
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Periodic Solutions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Coefficients

AbstractIn this work, under some conditions, we will prove that a scalar stochastic differential equation with periodic coefficients admits almost periodic solutions.

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