  This paper concernes with the existence of heteroclinic solutions for the
following class of elliptic equations $$ -\Delta{u}+A(\epsilon x, y)V'(u)=0,
\quad \mbox{in} \quad \Omega, $$ where $\epsilon >0$, $\Omega=\R \times \D$ is
an infinite cylinder of $\mathbb{R}^N$ with $N \geq 2$. Here, we have
considered a large class of potential $V$ that includes the Ginzburg-Landau
potential $V(t)=(t^{2}-1)^{2}$ and two geometric conditions on the function
$A$. In the first condition we assume that $A$ is asymptotic at infinity to a
periodic function, while in the second one $A$ satisfies $$
0<A_0=A(0,y)=\inf_{(x,y) \in \Omega}A(x,y) < \liminf_{|(x,y)| \to
+\infty}A(x,y)=A_\infty<\infty, \quad \forall y \in \D. $$
