Existence of quasiperiodic solutions of elliptic equations on RN+1 via center manifold and KAM theorems

Peter Polacik, Darío A. Valdebenito

Research output: Contribution to journalArticle

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We consider elliptic equations on RN+1 of the form Δxu+uyy+g(x,u)=0,(x,y)∈RN×R where g(x,u) is a sufficiently regular function with g(⋅,0)≡0. We give sufficient conditions for the existence of solutions of (1) which are quasiperiodic in y and decaying as |x|→∞ uniformly in y. Such solutions are found using a center manifold reduction and results from the KAM theory. We discuss several classes of nonlinearities g to which our results apply.

Original languageEnglish (US)
Pages (from-to)6109-6164
Number of pages56
JournalJournal of Differential Equations
Issue number12
StatePublished - Jun 15 2017


  • Center manifold
  • Elliptic equations
  • Entire solutions
  • KAM theorem
  • Nemytskii operators on Sobolev spaces
  • Quasiperiodic solutions

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