Existence of 2π-periodic solutions for nonlinear systems of first-order ordinary differential equations at resonance

1995 ◽  
Vol 25 (1) ◽  
pp. 1-16 ◽  
Author(s):  
R. Kent Nagle ◽  
Z. Sinkala
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
First Order ◽  
At Resonance

scholarly journals A New Method to Study the Periodic Solutions of the Ordinary Differential Equations Using Functional Analysis

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 677 ◽  
Author(s):  
Kadry ◽  
Alferov ◽  
Ivanov ◽  
Korolev ◽  
Selitskaya
Keyword(s):  
Functional Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Lower Bounds ◽  
New Method ◽  
Upper And Lower Bounds ◽  
First Order ◽  
Periodic Problems ◽  
Existence And Stability

In this paper, a new theorems of the derived numbers method to estimate the number of periodic solutions of first-order ordinary differential equations are formulated and proved. Approaches to estimate the number of periodic solutions of ordinary differential equations are considered. Conditions that allow us to determine both upper and lower bounds for these solutions are found. The existence and stability of periodic problems are considered.

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