Many solutions of elliptic problems on Rn of irrational slope

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 show that, under suitable hypotheses on F , this problem has a family of non-self-intersecting solutions u(D), which are at finite distance from a plane of slope (omega,0,...,0) with omega irrational. These solutions depend on a real parameter D; if D not equal D' , then the closures of the integer translates of u(D) and of u(D') do not intersect.