Theory of periodic solution

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I want to study the theory of the periodic solution of ordinary differential equations, but I don't know how to study. Could you give me some references?

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The following is a good list of textbooks for your purpose. Here is the best one:

A Modern Introduction to Differential Equations, 2nd Edition by Henry Ricardo

Paul Blanchard, Robert L. Devaney, Glenn R. Hall, Differential Equations (Preliminary Edition), PWS Publishing, Boston, 1996.

William H. Boyce and Richard C. Diprima, Elementary Differential Equations and Boundary Value Problems (6th Edition), Wiley, New York, 1996.

C.H. Edwards, Jr., David E. Penney, Elementary Dfifferential Equations with Applications (Third Edition), Prentice-Hall, Englewood Cliffs, NJ, 1996.

R. Kent Nagle and Edward B. Saff, Fundamentals of Differential Equations (Third Edition), Addison Wesley, Reading, MA, 1993.

Good luck!