Graduate School of Mathematical Sciences, The University of Tokyo
Journal of Mathematical Sciences, The University of Tokyo. Vol. 1 (1994), No. 3, Page 525-550
This paper studies certain classes of equations of the form $-Δ u=g(x, y, u)$ in an infinite strip (if $n=2$) or cylinder (if $n>2$). Variational arguments are used to establish the existence of solutions asymptotic to a pair of $x$-periodic states.