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.
|Number of pages||14|
|Journal||Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire|
|Publication status||Published - 2017|