Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773485 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2017 | 14 Pages |
Abstract
We consider entire solutions to Lu=f(u) in R2, where L is a nonlocal operator with translation invariant, even and compactly supported kernel K. Under different assumptions on the operator L, we show that monotone solutions are necessarily one-dimensional. The proof is based on a Liouville type approach. A variational characterization of the stability notion is also given, extending our results in some cases to stable solutions.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
François Hamel, Xavier Ros-Oton, Yannick Sire, Enrico Valdinoci,