Hongbin Chen and Yi Li 2008 Nonlinearity 21 2485 doi:10.1088/0951-7715/21/11/001
Hongbin Chen1 and Yi Li2
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We study the stability and exact multiplicity of periodic solutions of the Duffing equation from the global bifurcation point of view and show that the Duffing equation with cubic nonlinearities has at most three T-periodic solutions under a strong damped condition. More precisely, we prove that the T-periodic solutions form a smooth S-shaped curve and the stability of each T-periodic solution is determined by Floquet theory.
37K05 Hamiltonian structures, symmetries, variational principles, conservation laws
Issue 11 (November 2008)
Received 3 December 2007, in final form 2 September 2008
Published 29 September 2008
Hongbin Chen and Yi Li 2008 Nonlinearity 21 2485
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