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Ordinary Differential Equations and Applied Dynamics Commons™
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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
A Non-Autonomous Second Order Boundary Value Problem On The Half-Line, Gregory S. Spradlin
A Non-Autonomous Second Order Boundary Value Problem On The Half-Line, Gregory S. Spradlin
Greg S. Spradlin Ph.D.
By variational arguments, the existence of a solution to a nonautonomous second-order boundary problem on the half-line is proven. The corresponding autonomous problem has no solution, revealing significant differences between the autonomous and the non-autonomous case.
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.