  We give another proof of a theorem of Rabinowitz and Stredulinsky obtaining
infinite transition solutions for an Allen--Cahn equation. Rabinowitz and
Stredulinsky have constructed infinite transition solutions as locally minimal
solutions, but it is still an interesting question to establish these solutions
by other method. Our result may attract the interest of constructing solutions
with the shape of locally minimal solutions of Rabinowitz and Stredulinsky for
problems defined on descrete group.
