Electron. J. Diff. Eqns., Vol. 1999(1999), No. 42, pp. 1-12.

Infinitely many homoclinic orbits for Hamiltonian systems with group symmetries

Cheng Lee

This paper deals via variational methods with the existence of infinitely many homoclinic orbits for a class of the first-order time-dependent Hamiltonian systems
$$ \dot{z}=JH_z(t,z)  $$
without any periodicity assumption on $H$, providing that $H(t,z)$ is G-symmetric with respect to $z\in {\Bbb R}^{2N}$, is superquadratic as $|z|\to\infty$, and satisfies some additional assumptions.

Submitted March 19, 1999. Published October 12, 1999.
Math Subject Classifications: 34B30, 34C37.
Key Words: Hamiltonian system, homoclinic orbits.

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Cheng Lee
Department of Mathematics
National Changhua University of Education
Changhua, Taiwan. 50058 R.O.C.
e-mail address: clee@math.ncue.edu.tw
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