scholarly journals Existence and Stability of Almost Periodic Solutions for Quasilinear Delay Systems and the Halanay Inequality

2000 ◽  
Vol 248 (2) ◽  
pp. 625-644 ◽  
Author(s):  
Eduardo Liz ◽  
Sergei Trofimchuk
Keyword(s):  
Periodic Solutions ◽  
Delay Systems ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Halanay Inequality ◽  
Existence And Stability

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.

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