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Fink type conjecture on affine-periodic solutions and Levinson's conjecture to Newtonian systems

  • * Corresponding author: Yong Li

    * Corresponding author: Yong Li 
The first author is supported by National Basic Research Program of China (grant No. 2013CB834100), NSFC (grant No. 11571065) and NSFC (grant No. 11171132).The third author is supported by NSFC (grant No. 11201173).
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  • This paper concerns the existence of affine-periodic solutions for differential systems (including functional differential equations) and Newtonian systems with friction. This is a kind of pattern solutions in time-space, which may be periodic, anti-periodic, subharmonic or quasi periodic corresponding to rotation motions. Fink type conjecture is verified and Lyapunov's methods are given. These results are applied to study gradient systems and Newtonian (including Rayleigh or Lienard) systems. Levinson's conjecture to Newtonian systems is proved.

    Mathematics Subject Classification: Primary: 34C27; Secondary: 34C25.


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