Abstract
ABSTRACT We consider a class of periodic Allen–Cahn equations where is an even, periodic, positive function and is modeled on the classical two well Ginzburg–Landau potential . We show, via variational methods, that there exist infinitely many solutions, distinct up to periodic translations, of 1 asymptotic as to the pure states ±b, i.e., solutions satisfying the boundary conditions In fact, we prove the existence of solutions of 1-2 which are periodic in the y variable and if such solutions are finite modulo periodic translations, we can prove the existence of infinitely many (modulo periodic translations) solutions of 1-2 asymptotic to different periodic solutions as .
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