Abstract.
Using continuation methods and bifurcation theory, we study the exact multiplicity of periodic solutions, and the global solution structure, for a class of periodically forced pendulum-like equations. Our results apply also to the first order equations. We also show that by choosing a forcing term, one can produce periodic solutions with any number of Fourier coefficients arbitrarily prescribed.
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Korman, P. A global solution curve for a class of periodic problems, including the pendulum equation. Z. angew. Math. Phys. 58, 749–766 (2007). https://doi.org/10.1007/s00033-006-6014-6
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DOI: https://doi.org/10.1007/s00033-006-6014-6