We study stable solutions to the equation (− Δ) 1/2 u= f (u), posed in a bounded domain of R
n. For nonnegative convex nonlinearities, we prove that stable solutions are smooth in …

We study the extremal solutions of fractional Dirichlet problem $\begin {equation}\nonumber\
begin {cases}(-\Delta)^{s} u=\mu e^{v} &\mbox {in}\quad\Omega\\(-\Delta)^{s} …

In this paper we study the asymptotic behavior of sequences of stationary weak solutions to
the following Liouville-type equation $-\Delta u= e^ u~~~{in}~~~\Omega $, where $\Omega …

In this paper, we study the fractional Henon–Lane–Emden equation associated with Hardy
potential (–Δ) su–γ| x|-2 su=| x| ͣ| u| p–1 u in ℝ n. Extending the celebrated result of [14], we …

We classify finite Morse index solutions of the following Gelfand-Liouville equation (−∆) su=
eu in Rn, for 1< s< 2 and s= 2 via a novel monotonicity formula and technical blowdown …