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 $$ 0<A_0=A(0,y)=\inf_{ (x,y) \in \Omega}A(x,y) < \liminf_{ |(x,y)| \to +\infty}A(x,y)=A_\infty<\infty, \quad \forall y \in \D. $$
Categories: math.AP