# American Institute of Mathematical Sciences

January  2018, 38(1): 293-309. doi: 10.3934/dcds.2018014

## Limit periodic upper and lower solutions in a generic sense

 1 Universitá di Milano, via Saldini 50, 20133 Milano, Italy 2 NCMIS, RCSDS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

* Corresponding author: Zhe Zhou

Received  February 2017 Revised  July 2017 Published  September 2017

Fund Project: The second author is partially supported by the Key Lab of Random Complex Structures and Data Science, Chinese Academy of Sciences (Grant No. 2008DP173182) and the National Natural Science Foundation of China (Grant No. 11301512 and No. 11671382).

The method of upper and lower solutions is a main tool to prove the existence of periodic solutions to periodic differential equations. It is known that, in general, the method does not extend to the almost periodic case. The aim of the present paper is to show that, however, something interesting survives: if the classical assumptions of the method are satisfied, then the expected existence result holds generically in the limit periodic framework.

Citation: Massimo Tarallo, Zhe Zhou. Limit periodic upper and lower solutions in a generic sense. Discrete & Continuous Dynamical Systems, 2018, 38 (1) : 293-309. doi: 10.3934/dcds.2018014
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