Topological Methods in Nonlinear Analysis

Homoclinic orbits of first order nonlinear Hamiltonian systems with asymptotically linear nonlinearities at infinity

Guanwei Chen

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Abstract

By using variational methods and critical point theory, in particular, a generalized weak linking theorem, we study a first order nonlinear Hamiltonian system with asymptotically linear nonlinearity at infinity. We obtain the existence of ground state homoclinic orbits for this nonlinear Hamiltonian system. In particular, we obtain a necessary and sufficient condition for the existence of ground state homoclinic orbits. To the best of our knowledge, there is no published result focusing on necessary and sufficient conditions of the existence of ground state homoclinic orbits for this system.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 47, Number 2 (2016), 499-510.

Dates
First available in Project Euclid: 13 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1468413749

Digital Object Identifier
doi:10.12775/TMNA.2016.038

Mathematical Reviews number (MathSciNet)
MR3559623

Zentralblatt MATH identifier
1361.37060

Citation

Chen, Guanwei. Homoclinic orbits of first order nonlinear Hamiltonian systems with asymptotically linear nonlinearities at infinity. Topol. Methods Nonlinear Anal. 47 (2016), no. 2, 499--510. doi:10.12775/TMNA.2016.038. https://projecteuclid.org/euclid.tmna/1468413749


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