We consider a class of
semilinear elliptic equations of the form
15.7cm
-$\varepsilon^{2}\Delta u(x,y)+a(x)W'(u(x,y))=0,\quad (x,y)\in{\mathbb{R}}^{2}$
where $\varepsilon>0$
, $a:{\mathbb{R}}\to{\mathbb{R}}$
is a periodic, positive function and
$W:{\mathbb{R}}\to{\mathbb{R}}$
is modeled on the classical two well Ginzburg-Landau
potential $W(s)=(s^{2}-1)^{2}$
. We look for solutions to ([see full textsee full text])
which verify the
asymptotic conditions $u(x,y)\to\pm 1$
as $x\to\pm\infty$
uniformly with respect to $y\in{\mathbb{R}}$
.
We show via variational
methods that if ε is sufficiently small and a is not constant,
then ([see full textsee full text])
admits infinitely many of such solutions, distinct up to translations,
which do not exhibit one dimensional symmetries.