Abstract
<div class="line" id="line-29"> We study the differential equation ¨x(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| → ∞. 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 → −∞ 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| → ∞.</div>
Original language | American English |
---|---|
Journal | Electronic Journal of Differential Equations |
Volume | 2010 |
State | Published - 2010 |
Keywords
- heteroclinic
- non-autonomous equation
- bounded solution
- variational methods
Disciplines
- Ordinary Differential Equations and Applied Dynamics