  In this paper we show the existence of strictly monotone heteroclinic type
solutions of semilinear elliptic equations in cylinders. The motivation of this
construction is twofold: first, it implies the existence of an entire bounded
solution of a semilinear equation without critical points which is not
one-dimensional. Second, this gives an example of a bounded stationary solution
for the 2D Euler equations without stagnation points which is not a shear flow,
completing previous results of Hamel and Nadirashvili. The proof uses a
minimization technique together with a truncation argument, and a limit
procedure.
