Many Solutions of Elliptic Problems on R n of Irrational Slope |
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Authors: | Ugo Bessi |
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Institution: | 1. Dipartimento di Matematica , Università Roma Tre , Roma, Italy bessi@matrm3.mat.uniroma3.it |
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Abstract: | ABSTRACT 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. |
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Keywords: | Aubry-Mather theory for elliptic problems on R n Minimal and non-self intersecting solutions Multiplicity for Denjoy sets |
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