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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Homoclinic orbits of superlinear Hamiltonian systems
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by Guanwei Chen and Shiwang Ma PDF
Proc. Amer. Math. Soc. 139 (2011), 3973-3983 Request permission

Abstract:

In this paper, we consider the first-order Hamiltonian system \[ J\dot {u}(t)+\nabla H(t,u(t))=0,\quad t\in \mathbb {R}. \] Here the classical Ambrosetti-Rabinowitz superlinear condition is replaced by a general super-quadratic condition. We will study the homoclinic orbits for the system. The main idea here lies in an application of a variant generalized weak linking theorem for a strongly indefinite problem developed by Schechter and Zou.
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Additional Information
  • Guanwei Chen
  • Affiliation: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People’s Republic of China
  • Email: guanweic@163.com
  • Shiwang Ma
  • Email: shiwangm@163.net
  • Received by editor(s): September 17, 2010
  • Published electronically: May 25, 2011
  • Additional Notes: Research supported by the Specialized Fund for the Doctoral Program of Higher Education and the National Natural Science Foundation of China.
  • Communicated by: Matthew J. Gursky
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3973-3983
  • MSC (2010): Primary 37J45, 37K05, 58E05
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11185-7
  • MathSciNet review: 2823043