conditionally periodic function
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2020 ◽  
Vol 72 (4) ◽  
pp. 56-62
Author(s):  
Zh. Suleimenov ◽  
◽  
S.K. Kuanysh ◽  

In the theory of nonlinear oscillations one often encounters conditionally periodic oscillations resulting from the superposition of several oscillations with frequencies incommensurable with each other. When finding a solution to a resonant quasilinear differential system in the form of a conditionally periodic function, the problem of a small denominator arises. Consequently, the proof of the existence and even more the construction of such a solution is not an easy task. In this article, drawing on the work of V.I. Arnold, I. Moser, and other researchers proved the existence and constructed a conditionally periodic solution of a second-order quasilinear differential system in the critical case. Accelerated convergence method by N.N. Bogolyubova, Yu.A. Mitropolsky, A.M. Samoylenko. The result can be applied to construct a conditionally periodic solution of specific differential systems.



1998 ◽  
Vol 63 (5) ◽  
pp. 648-657 ◽  
Author(s):  
N. G. Moshchevitin


1997 ◽  
Vol 61 (4) ◽  
pp. 473-479 ◽  
Author(s):  
S. V. Konyagin




1991 ◽  
Vol 50 (3) ◽  
pp. 945-952
Author(s):  
N. G. Moshchevitin


1991 ◽  
Vol 49 (6) ◽  
pp. 650-652 ◽  
Author(s):  
N. G. Moshchevitin


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