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Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
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.
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.
An Elliptic Equation With No Monotonicity Condition On The Nonlinearity, Gregory S. Spradlin
An Elliptic Equation With No Monotonicity Condition On The Nonlinearity, Gregory S. Spradlin
Greg S. Spradlin Ph.D.
An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle degree theory argument must be used.
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.
An Elliptic Partial Differential Equation With A Symmetrical Almost Periodic Term, Gregory S. Spradlin
An Elliptic Partial Differential Equation With A Symmetrical Almost Periodic Term, Gregory S. Spradlin
Greg S. Spradlin Ph.D.
No abstract provided.
A Singularly Perturbed Elliptic Partial Differential Equation With An Almost Periodic Term, Gregory S. Spradlin
A Singularly Perturbed Elliptic Partial Differential Equation With An Almost Periodic Term, Gregory S. Spradlin
Greg S. Spradlin Ph.D.
No abstract provided.