Interfering solutions of a nonhomogeneous Hamiltonian system

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.

Keywords

• Variational methods
• minimax argument
• nonhomogeneous linearity
• Hamiltonian system
• Nehari manifold.