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Existence and non-existence of periodic solutions of generalized Lineard equations with damping of no lower bound

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Abstract

This paper establishes criteria for the existence and non-existence of nonzero periodic solutions of the generalized Liénard equationx +f(x,x)x +g(x)=0. The main goal is to study to what extent the dampingf can be small so as to guarantee the existence of nonzero periodic solutions of such a system. With some standard additional assumptions we prove that if for a small ¦x¦, ∫±∞ ¦f(x,y)¦−1 dy=±∞, then the system has at least one nonzero periodic solution, otherwise, the system has no nonzero periodic solution. Many classical and well-known results can be proved as corollaries to ours.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, 230026, Hefei, China

    Jiang Jifa

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  1. Jiang Jifa
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Supported by the National Natural Science Foundation of China.

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Jifa, J. Existence and non-existence of periodic solutions of generalized Lineard equations with damping of no lower bound. Acta Mathematica Sinica 12, 361–371 (1996). https://doi.org/10.1007/BF02106790

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  • DOI: https://doi.org/10.1007/BF02106790

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