scholarly journals New results on positive almost periodic solutions for first-order neutral differential equations

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Yuehua Yu ◽  
Shuhua Gong
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Neutral Differential Equations ◽  
First Order ◽  
Positive Almost Periodic Solutions

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.

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.

scholarly journals Existence of Almost Periodic Solutions to th-Order Neutral Differential Equations with Piecewise Constant Arguments

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Rong-Kun Zhuang
Keyword(s):  
Positive Integer ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Existence And Uniqueness ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Neutral Differential Equations ◽  
Greatest Integer Function

We present some conditions for the existence and uniqueness of almost periodic solutions of th-order neutral differential equations with piecewise constant arguments of the form , here is the greatest integer function, and are nonzero constants, is a positive integer, and is almost periodic.

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