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Multiple solutions for indefinite functionals and applications to asymptotically linear problems

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Abstract

In this paper, by means of Morse theory of isolated critical points (orbits) we study further the critical points theory of asymptotically quadratic functionals and give some results concerning the existence of multiple critical points (orbits) which generalize a series of previous results due to Amann, Conley, Zehnder and K.C. Chang. As applications, the existence of multiple periodic solutions for asymptotically linear Hamiltonian systems is investigated. And our results generalize some recent ones due to Coti-Zelati, J.Q.Liu, S.Li, etc.

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References

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Authors and Affiliations

  1. Department of Mathematics, Peking University, China

    Wang Zhiqiang

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  1. Wang Zhiqiang
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This research was supported in part by the National Postdoctoral Science Fund.

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Zhiqiang, W. Multiple solutions for indefinite functionals and applications to asymptotically linear problems. Acta Mathematica Sinica 5, 101–113 (1989). https://doi.org/10.1007/BF02107664

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