Periodic solutions of nonlinear differential systems by the method of averaging

2020 ◽  
Vol 65 (4) ◽  
pp. 511-542
Author(s):  
Zhanyong Li ◽  
Qihuai Liu ◽  
Kelei Zhang
Keyword(s):  
Periodic Solutions ◽  
Method Of Averaging ◽  
Differential Systems ◽  
Nonlinear Differential Systems

scholarly journals ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR A CLASS OF NONLINEAR DIFFERENTIAL SYSTEMS

1993 ◽  
Vol 24 (2) ◽  
pp. 173-188
Author(s):  
LIHONG HUANG ◽  
JIANSHE YU
Keyword(s):  
Periodic Solutions ◽  
Special Form ◽  
Differential Systems ◽  
Nontrivial Periodic Solutions ◽  
Existence Of Periodic Solutions ◽  
Nonlinear Differential Systems

In this paper three theorems on the existence of nontrivial periodic solutions of the system \[ dx/dt =e(y)\]\[dy/dt =-e(y)f(x)- g(x)\] are proved, which not only generalize some known results on the existence of periodic solutions of Lienard's system (i.e. the special form for $e(y) = y$), but also relax or eliminate some traditional assumptions.

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