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Existence of solutions for sub-linear or super-linear operator equations

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Abstract

We investigate solutions to superlinear or sublinear operator equations and obtain some abstract existence results by minimax methods. These results apply to superlinear or sublinear Hamiltonian systems satisfying several boundary value conditions including Sturm-Liouville boundary value conditions and generalized periodic boundary value conditions, and yield some new theorems concerning existence of solutions or nontrivial solutions. In particular, some famous results about periodic solutions to superlinear or sublinear Hamiltonian systems by Rabinowitz or Benci-Rabinowitz are special cases of the theorems.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing Normal University, Nanjing, 210097, China

    YingYing Chen & YuJun Dong

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, China

    Yuan Shan

Authors
  1. YingYing Chen
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  2. YuJun Dong
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  3. Yuan Shan
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Correspondence to YuJun Dong.

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Chen, Y., Dong, Y. & Shan, Y. Existence of solutions for sub-linear or super-linear operator equations. Sci. China Math. 58, 1653–1664 (2015). https://doi.org/10.1007/s11425-014-4966-0

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  • DOI: https://doi.org/10.1007/s11425-014-4966-0

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