Heteroclinics for non autonomous third order differential equations
Résumé
We study the existence of heteroclinics connecting the two equilibria $\pm1$ of the third order differential equation
$$u'''=f(u)+p(t)u'$$
where $f$ is a continuous function such that $f(u)(u^2-1)> 0$ if $u\neq\pm1$ and
$p$ is a bounded non negative function.
Uniqueness is also addressed.