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Full-Text Articles in Physical Sciences and Mathematics
Heteroclinic Solutions To An Asymptotically Autonomous Second-Order Equation, Gregory S. Spradlin
Heteroclinic Solutions To An Asymptotically Autonomous Second-Order Equation, Gregory S. Spradlin
Mathematics - Daytona Beach
We study the differential equation ẍ(t) = a(t)V '(x(t)), where V is a double-well potential with minima at x = ±1 and a(t) →l > 0 as |t| → 1. It is proven that under certain additional assumptions on a, there exists a heteroclinic solution x to the differential equation with x(t) → -1 as t → -1 and x(t) → 1 as t → ∞. The assumptions allow l - a(t) to change sign for arbitrarily large values of |t|, and do not restrict the decay rate of |l -a(t)| as |t| → ∞ © 2010 Texas State University - …
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
Mathematics - Daytona Beach
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. © EDP Sciences, SMAI 2007.
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
Mathematics - Daytona Beach
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. © EDP Sciences, SMAI 2006.