### On the existence of heteroclinic trajectories for asymptotically autonomous equations

DOI: http://dx.doi.org/10.12775/TMNA.2009.041

#### Abstract

By means of a minimax argument, we prove the existence

of at least one heteroclinic solution to a scalar equation

of the kind $\ddot x=a(t)V'(x)$, where $V$ is a double well potential,

$0< l\le a(t)\le L$, $a(t)\to l$ as $|t|\to\infty$ and the ratio $L/l$

is suitably bounded from above.

of at least one heteroclinic solution to a scalar equation

of the kind $\ddot x=a(t)V'(x)$, where $V$ is a double well potential,

$0< l\le a(t)\le L$, $a(t)\to l$ as $|t|\to\infty$ and the ratio $L/l$

is suitably bounded from above.

#### Keywords

Heteroclinic; double-well potential; minimax

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