  Block copolymer, a synthesized polymer material, has found many applications
in industry. It is consisting of multiple sequences of monomer alternating in
series with different monomer blocks. The combination of different polymers
endows the polymer material with rich properties, which are the key to their
important applications. In this paper, we model the copolymers with
Landau-Brazovskii model with additional constraints reflecting physical
structures, which is in the form of a second order variational problem.
Critical points of the functional are interpreted as states of polymers. By
reducing to handy situations, we find a nontrivial periodic minimal solution.
Moreover, the proof is kept as simple and self-contained as possible in our
specific case.
