Exact Multiplicity and Stability of Periodic Solutions for Duffing Equation with Bifurcation Method
Exact Multiplicity and Stability of Periodic Solutions for Duffing Equation with Bifurcation Method
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DOI：
10.1007/s12346-018-0296-x
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发表时间：
--
影响因子：
1.4
通讯作者：
梁树青
中科院分区：
文献类型：
--
作者：
梁树青
Under some LpLp-norms(p∈[1,∞]p∈[1,∞]) assumptions for the derivative of the restoring force, the exact multiplicity and the stability of 2π2π-periodic solutions for Duffing equation are considered. The nontrivial 2π2π-periodic solutions of it are positive or negative, and the bifurcation curve of it is a unique reversed S-shaped curve. The class of the restoring force is extended, comparing with the class of L∞L∞-norm condition. The proof is based on the global bifurcation theorem, topological degree and the estimates for periodic eigenvalues of Hill’s equation by LpLp-norms(p∈[1,∞]p∈[1,∞]).
