## Solutions of heteroclinic type for some classes of semilinear elliptic partial differential equations

J. Math. Sci. Univ. Tokyo
Vol. 1 (1994), No. 3, Page 525--550.

Rabinowitz, Paul H.
Solutions of heteroclinic type for some classes of semilinear elliptic partial differential equations
This paper studies certain classes of equations of the form $-Î u=g(x, y, u)$ 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.