Existence and stability of almost periodic solutions of nonautonomous competitive systems with weak Allee effect and delays

2009 ◽  
Vol 14 (11) ◽  
pp. 3993-4002 ◽  
Author(s):  
Wanqin Wu ◽  
Yuan Ye
Keyword(s):  
Periodic Solutions ◽  
Allee Effect ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Competitive Systems ◽  
Existence And Stability

Almost periodic solutions of nonautonomous Lotka–Volterra competitive systems with dominated delays

2015 ◽  
Vol 08 (02) ◽  
pp. 1550019 ◽  
Author(s):  
Chunhua Feng ◽  
Jianmin Huang
Keyword(s):  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Volterra System ◽  
Volterra Type ◽  
Competitive Systems

In this paper, a class of nonautonomous Lotka–Volterra type multispecies competitive systems with delays is studied. By employing Lyapunov functional, some sufficient conditions to guarantee the existence of almost periodic solutions for the Lotka–Volterra system are obtained.

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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