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Existence of Periodic Solutions of Linear Hamiltonian Systems with Sublinear Perturbation

Abstract

We investigate the existence of periodic solutions of linear Hamiltonian systems with a nonlinear perturbation. Under generalized Ahmad-Lazer-Paul type coercive conditions for the nonlinearity on the kernel of the linear part, existence of periodic solutions is obtained by saddle point theorems. A note on a result of Rabinowitz is also given.

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Correspondence to Zhiqing Han.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Han, Z. Existence of Periodic Solutions of Linear Hamiltonian Systems with Sublinear Perturbation. Bound Value Probl 2010, 945421 (2010). https://doi.org/10.1155/2010/945421

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Periodic Solution
  • Functional Equation