Two-bubble nodal solutions for slightly subcritical Fractional Laplacian

Abstract: In this paper, we consider the existence of nodal solutions with two bubbles to the slightly subcritical problem with the fractional Laplacian \begin{equation*} \left{\aligned &(-\Delta)^su=|u|^{p-1-\varepsilon}u\ \ \mbox{in}\ \Omega &u=0\ \mbox{on}\ \partial\Omega, \endaligned \right. \end{equation*} where $\Omega$ is a smooth bounded domain in $\mathbb R^N$, $N>2s$, $0<s\<1$, $ p=\frac{N+2s}{N-2s}$ and $\varepsilon\>0$ is a small parameter, which can be seen as a nonlocal analog of the results of Bartsch, Micheletti and Pistoia (2006) \cite{Bartsch1}.