Heteroclinic Solutions to an Asymptotically Autonomous Second-Order Equation

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Abstract

<div class="line" id="line-29"> We study the di&fflig;erential equation &uml;x(t) = a(t)V' (x(t)), where V is a double-well potential with minima at x = &plusmn;1 and a(t) &rarr; l &gt; 0 as |t| &rarr; &infin;. It is proven that under certain additional assumptions on a, there exists a heteroclinic solution x to the di&fflig;erential equation with x(t) &rarr; &minus;1 as t &rarr; &minus;&infin; and x(t) &rarr; 1 as t &rarr; &infin;. The assumptions allow l &minus; a(t) to change sign for arbitrarily large values of |t|, and do not restrict the decay rate of |l &minus;a(t)| as |t| &rarr; &infin;.</div>
Original languageAmerican English
JournalElectronic Journal of Differential Equations
Volume2010
StatePublished - 2010

Keywords

  • heteroclinic
  • non-autonomous equation
  • bounded solution
  • variational methods

Disciplines

  • Ordinary Differential Equations and Applied Dynamics

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