Many Solutions of Elliptic Problems on Rnof Irrational Slope
Ugo Bessi · Communications in Partial Differential Equations · 2005
We consider the problem − Δ 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 (ω,0,…,0) with ω irrational. These solutions depend on a real parameter D; if D ≠ D ′, then the closures of the integer translates of u D and of u D ′ do not intersect.