Lyapunov stability of periodic solutions of the quadratic Newtonian equation |
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| Authors: | Meirong Zhang Jifeng Chu Xiong Li |
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| Affiliation: | 1. Department of Mathematical Sciences, Tsinghua University, Beijing 100084, P. R. China;2. Phone: +86 25 8378 0880, Fax: +86 25 8378 6626;3. Department of Mathematics, Beijing Normal University, Beijing 100875, P. R. China;4. Phone: +86 10 5880 7735 |
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| Abstract: | We will find a positive constant Σ2 such that for any 2π ‐periodic function h (t) with zero mean value, the quadratic Newtonian equation x ″ + x2 = σ + h (t) will have exactly two 2π ‐periodic solutions with one being unstable and another being twist (and therefore being Lyapunov stable), provided that the parameter σ is bigger than the first bifurcation value and is smaller than the constant Σ2. The construction of Σ2 is obtained by examining carefully the twist coefficients of periodic solutions (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Lyapunov stability periodic solution quadratic equation twist coefficient |
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