Stability and exact multiplicity of periodic solutions of Duffing equations with cubic nonlinearities |
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| Authors: | Hongbin Chen Yi Li |
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| Affiliation: | Department of Mathematics, Xi'an Jiaotong University, Xi'an, People's Republic of China ; Department of Mathematics, Hunan Normal University, Changsha, Hunan, People's Republic of China |
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| Abstract: | We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities, where  and  are positive constants and  is a positive  -periodic function. We obtain sharp bounds for  such that  has exactly three ordered  -periodic solutions. Moreover, when  is within these bounds, one of the three solutions is negative, while the other two are positive. The middle solution is asymptotically stable, and the remaining two are unstable. |
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| Keywords: | Duffing equation periodic solution stability |
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