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Some notes on a superlinear second order Hamiltonian system

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Abstract

Variational methods are used in order to establish the existence and the multiplicity of nontrivial periodic solutions of a second order dynamical system. The main results are obtained when the potential satisfies different superquadratic conditions at infinity. The particular case of equations with a concave-convex nonlinear term is covered.

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Authors and Affiliations

  1. Department of Engineering, University of Messina, c.da Di Dio Sant’Agata, 98166, Messina, Italy

    Gabriele Bonanno

  2. Department DICEAM, University of Reggio Calabria, 89100, Reggio Calabria, Italy

    Roberto Livrea

  3. Department of Mathematics, University of California, Irvine, CA, 92697-3875, USA

    Martin Schechter

Authors
  1. Gabriele Bonanno
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  2. Roberto Livrea
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  3. Martin Schechter
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Correspondence to Gabriele Bonanno.

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Bonanno, G., Livrea, R. & Schechter, M. Some notes on a superlinear second order Hamiltonian system. manuscripta math. 154, 59–77 (2017). https://doi.org/10.1007/s00229-016-0903-6

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  • DOI: https://doi.org/10.1007/s00229-016-0903-6

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