Slope-changing solutions of elliptic problems on $\R^n$.

We consider the problem $-\Delta u+F_u(x,u)=0$ on $\R^n$, where $F$ is a smooth function periodic of period 1 in all its variables. We are going to find a nondegeneracy condition on $F$ for which the following holds. If we are given a sequence of positive integers $\{ \tilde N_i \}_{i\in\Z}$ and a sequence $\{ \a_i \}_{i\in\Z}$ of real numbers (the slopes), then we shall find an increasing sequence $\{ Q_i\}$ of integers and a solution $u$ which is entire, periodic in $(x_2,\dots,x_n)$ and which is close to the plane $\a_1(x_1-Q_i)+u(Q_i,0,\dots,0)$ for $x_1\in [Q_i,Q_i+\tilde N_i]$.