Geodesic
Homoclinic orbits for a class of symmetric Hamiltonian systems
Electronic journal of differential equations, Tome 1994 (1994) no. 1
We study existence of homoclinic orbits for a class of Hamiltonian systems that are symmetric with respect to independent variable (time). For the scalar case we prove existence and uniqueness of a positive homoclinic solution. For the system case we prove existence of symmetric homoclinic orbits. We use variational approach.
Classification : 34B15, 34A34
Keywords: homoclinic orbits, mountain-pass lemma 
@article{EJDE_1994__1994_1_a0,
     author = {Korman,  Philip and Lazer,  Alan C.},
     title = {Homoclinic orbits for a class of symmetric {Hamiltonian} systems},
     journal = {Electronic journal of differential equations},
     year = {1994},
     volume = {1994},
     number = {1},
     zbl = {0788.34042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1994__1994_1_a0/}
}
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Korman,  Philip; Lazer,  Alan C. Homoclinic orbits for a class of symmetric Hamiltonian systems. Electronic journal of differential equations, Tome 1994 (1994) no. 1. http://geodesic.mathdoc.fr/item/EJDE_1994__1994_1_a0/