Electron. J. Diff. Eqns. Vol. 1994(1994), No. 01, pp. 1-10.

Homoclinic Orbits for a Class of Symmetric Hamiltonian Systems

Philip Korman & Alan C. Lazer

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.

Submitted October 22, 1993. Published February 15, 1994.
Math Subject Classification: 34B15, 34A34.
Key Words: Homoclinic orbits, mountain-pass lemma.

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Philip Korman
Institute for Dynamics and Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA
e-mail: korman@ucbeh.san.uc.edu

Alan C. Lazer
Department of Mathematics and Computer Science, University of Miami, Coral Gables, FL 33124, USA
e-mail: lazer@mthvax.cs.miami.edu

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