Boundary blow-up solutions in the unit ball : asymptotics, uniqueness and symmetry

We calculate the full asymptotic expansion of boundary blow-up so- lutions, for any nonlinearity f . Our approach enables us to state sharp qualitative results regarding uniqueness and ra- dial symmetry of solutions, as well as a characterization of nonlinearities for which the blow-up rate is universal. At last, we study in more detail the standard nonlinearities f (u) = u^p, p >

On the fractional Lane-Emden equation

We classify solutions of finite Morse index of the fractional Lane- Emden equatio

Online Appendix to "Technology shocks around the world"

This appendix presents several robustness experiments, carried on actual and simulated data.

Uniqueness of large solutions

Given a nondecreasing nonlinearity $f$, we prove uniqueness of large solutions in the following two cases: the domain is the ball or the domain has nonnegative mean curvature and the nonlinearity is asymptotically convex

Regularity of radial extremal solutions for some non local semilinear equations

We investigate stable solutions of elliptic equations of the type \begin{equation*} \left \{ \begin{aligned} (-\Delta)^s u&=\lambda f(u) \qquad {\mbox{ in $B_1 \subset \R^{n}$}} \\ u&= 0 \qquad{\mbox{ on $\partial B_1$,}}\end{aligned}\right . \end{equation*} where $n\ge2$, $s \in (0,1)$, $\lambda \geq 0$ and $f$ is any smooth positive superlinear function. The operator $(-\Delta)^s$ stands for the fractional Laplacian, a pseudo-differential operator of order $2s$. According to the value of $\lambda$, we study the existence and regularity of weak solutions $u$