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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Homoclinic orbits of superlinear Hamiltonian systems


Authors: Guanwei Chen and Shiwang Ma
Journal: Proc. Amer. Math. Soc. 139 (2011), 3973-3983
MSC (2010): Primary 37J45, 37K05, 58E05
Published electronically: May 25, 2011
MathSciNet review: 2823043
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we consider the first-order Hamiltonian system

$\displaystyle 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
Affiliation: School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, People’s Republic of China
Email: shiwangm@163.net

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11185-7
PII: S 0002-9939(2011)11185-7
Keywords: Homoclinic orbit, first-order Hamiltonian system, ground state solution, concentration compactness principle.
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.