Heteroclinic Solutions to an Asymptotically Autonomous Second-Order EquationElectronic Journal of Differential Equations (2010)
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| → ∞.
- non-autonomous equation,
- bounded solution,
- variational methods
Citation InformationGregory S. Spradlin. "Heteroclinic Solutions to an Asymptotically Autonomous Second-Order Equation" Electronic Journal of Differential Equations Vol. 2010 Iss. 137 (2010) p. 1 - 14 ISSN: 1072-6691
Available at: http://works.bepress.com/greg_spradlin/4/