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Periodic solutions of second order equations with asymptotical non-resonance

  • * Corresponding author: Dingbian Qian

    * Corresponding author: Dingbian Qian 
This work was supported by National Natural Science Foundation of China (No.11671287, No.61573228)
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  • This paper deals with the periodic solutions of second order equations with asymptotical non-resonance. Using the point of view that the force is a perturbation, we can think that, asymptotically, the solutions of forced non-autonomous equation behave as those of the autonomous equation. Then, under a sharp integral condition, we prove that the periodic solution of non-autonomous equation can be estimated by using time map of autonomous equation. The existence of periodic solutions is thus proved via qualitative analysis and topological degree theory. The main result in this paper generalize a existence result obtained by Capietto, Mawhin and Zanolin.

    Mathematics Subject Classification: Primary: 34C25, 34B15; Secondary: 54D25.


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  •   A. Capietto , J. Mawhin  and  F. Zanolin , Continuation theorems for periodic perturbations of autonomous systems, Trans. Amer. Math. Soc., 329 (1992) , 41-72.  doi: 10.1090/S0002-9947-1992-1042285-7.
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      D. Qian , Time-maps and Duffing equations across resonance, Science in China A, 23 (1993) , 471-479. 
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