Electron. J. Diff. Eqns., Vol. 2001(2001), No. 47, pp. 1-10.

Interfering solutions of a nonhomogeneous Hamiltonian system

Gregory S. Spradlin

Abstract:
A Hamiltonian system is studied which has a term approaching a constant at an exponential rate at infinity . A minimax argument is used to show that the equation has a positive homoclinic solution. The proof employs the interaction between translated solutions of the corresponding homogeneous equation. What distinguishes this result from its few predecessors is that the equation has a nonhomogeneous nonlinearity.

Submitted April 30, 2001. Published June 21, 2001.
Math Subject Classifications: 35A15.
Key Words: Variational methods, minimax argument, nonhomogeneous linearity, Hamiltonian system, Nehari manifold.

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Gregory S. Spradlin
Department of Computing and Mathematics
Embry-Riddle Aeronautical University
Daytona Beach, Florida 32114-3900 USA
e-mail: spradlig@erau.edu

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