Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 47, pp. 1-10.
Title: Interfering solutions of a nonhomogeneous Hamiltonian system
Author: Gregory S. Spradlin (Embry-Riddle Aeronautical Univ. Daytona Beach, FL, USA)
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.