Brake orbits type solutions to some class of semilinear elliptic equations

We consider a class of semilinear elliptic equations of the form $$-\Delta u(x,y)+a(x)W'(u(x,y))=0,\quad (x,y)\in\R^{2}$$ where $a:\R\to\R$ is a periodic, positive function and $W:\R\to\R$ is modeled on the classical two well Ginzburg-Landau potential $W(s)=(s^{2}-1)^{2}$. We show, via variational methods, that if the set of solutions to the one dimensional heteroclinic problem $$-\ddot q(x)+a(x)W'(q(x))=0,\ x\in\R,\qquad q(\pm\infty)=\pm 1,$$ has a discrete structure, then the equation has infinitely many solutions periodic in the variable $y$ and verifying the asymptotic conditions $u(x,y)\to\pm 1$ as $x\to\pm\infty$ uniformly with respect to $y\in\R$.