| Abstract: |
| Our interest in the present talk is to deal with nonlocal problems posed in the whole real line $\R$
\begin{equation}\label{eq-problema}
(-\Delta)^s u = f(u) \quad \text{in } \mathbb{R}.
\end{equation}
Particular types of solutions have been obtained for problem \eqref{eq-problema} depending on
the `shape` of the nonlinearity. For instance, layer solutions or ground states. However, at the best of our knowledge,
the existence of periodic solutions to \eqref{eq-problema} has not been obtained so far except
for a very particular $f$. We will introduce a suitable framework which
allows to reduce the search for such periodic solutions to the resolution of a boundary
value problem in a suitable Hilbert space, thereby making it possible to reach for the
usual tools of nonlinear analysis, like bifurcation theory or variational methods.
We obtain some existence theorems which are lately enlightened with the analysis of some
examples. |
|