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Zeitschrift für Analysis und ihre Anwendungen


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Volume 34, Issue 1, 2015, pp. 27–41
DOI: 10.4171/ZAA/1527

Published online: 2015-01-08

Existence of Homoclinic Orbits of Superquadratic Second-Order Hamiltonian Systems

Chengjun Guo[1], Donal O'Regan[2], Chengjiang Wang[3] and Ravi P. Agarwal[4]

(1) Guangdong University of Technology, Guangzhou, China
(2) National University of Ireland, Galway, Ireland
(3) Guangdong University of Technology, Guangzhou, China
(4) Texas A&M University, Kingsville, United States

Using critical point theory, we study the existence of homoclinic orbits for the second-order Hamiltonian system $$\ddot{z}-K_{z}(t,z)+V_{z}(t,z)=h(t), $$ where $V(t,z)$ depends periodically on $t$ and is superquadratic.

Keywords: Homoclinic orbit, Hamiltonian system, critical point theory

Guo Chengjun, O'Regan Donal, Wang Chengjiang, Agarwal Ravi: Existence of Homoclinic Orbits of Superquadratic Second-Order Hamiltonian Systems. Z. Anal. Anwend. 34 (2015), 27-41. doi: 10.4171/ZAA/1527