**Chengjun Guo, Ravi P. Agarwal, Chengjiang Wang, and Donal O'Regan**

##
The Existence of Homoclinic Orbits for a Class of First-Order Superquadratic
Hamiltonian Systems

**abstract:**

Using critical point theory, we study the existence of homoclinic orbits for the
first-order superquadratic Hamiltonian system

$$ \dot{z}=JH_{z}(t,z), $$

where $H(t,z)$ depends periodically on $t$ and is superquadratic.

**Mathematics Subject Classification:**
34K13, 34K18, 58E50

**Key words and phrases:** Homoclinic orbit, Hamiltonian system, critical
point theory