Interfering Solutions of a Nonhomogeneous Hamiltonian System
Spradlin, Gregory S.
Southwest Texas State University, Department of Mathematics
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.
Variational methods, Minimax argument, Nonhomogeneous linearity, Hamiltonian system, Nehari manifold
Spradlin, G. S. (2001). Interfering solutions of a nonhomogeneous Hamiltonian system. <i>Electronic Journal of Differential Equations, 2001</i>(47), pp. 1-10.