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Full-Text Articles in Physical Sciences and Mathematics
Scattered Homoclinics To A Class Of Time-Recurrent Hamiltonian Systems, Gregory S. Spradlin
Scattered Homoclinics To A Class Of Time-Recurrent Hamiltonian Systems, Gregory S. Spradlin
Greg S. Spradlin Ph.D.
A second-order Hamiltonian system with time recurrence is studied. The recurrence condition is weaker than almost periodicity. The existence is proven of an infinite family of solutions homoclinic to zero whose support is spread out over the real line.
Interfering Solutions Of A Nonhomogeneous Hamiltonian System, Gregory S. Spradlin
Interfering Solutions Of A Nonhomogeneous Hamiltonian System, Gregory S. Spradlin
Greg S. Spradlin Ph.D.
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.