Slope-changing solutions of elliptic problems on Rn

We consider the problem −Δu+Fu(x,u)=0 on Rn, where F is a smooth function periodic of period 1 in all its variables. We are going to find a non-degeneracy condition on F for which the following holds. If we are given a sequence of positive integers {Ñi}i∈Z and a sequence {αi}i∈Z of real numbers (the slopes), then we shall find an increasing sequence {Qi} of integers and a solution u which is entire, periodic in (x2,…,xn) and which is close to the plane α1(x1−Qi)+u(Qi,0,…,0) for x1∈[Qi,Qi+Ñi].