## 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.## References

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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