# Morse Index for fractional laplacian

Is there any information on the Morse Index of the least energy solution of $(-\Delta)^s u= f(u) \text{ in } \Omega; u=0 \text{ in } \mathbb{R}^N-\Omega.$

The Morse index for a solution obtained by the mountain pass theorem is less than equal to one in the case of laplacian. Is it true for the fractional Laplace case. For example if we consider $f(u)\sim u^{p}$.
• What kind of information are you looking for? The solution $u$ may behave in an unexpected way, for example, it may have local minima in $\Omega$ even if $f > 0$. – Mateusz Kwaśnicki Aug 11 '17 at 11:44