We prove sharp blow up rates of solutions of higher order conformally invariant equations in
a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of …

We establish uniqueness of vanishing radially decreasing entire solutions, which we call
ground states, to some semilinear fractional elliptic equations. In particular, we treat the …

This manuscript is devoted to constructing complete metrics with constant higher fractional
curvature on punctured spheres with finitely many isolated singularities. Analytically, this …

We prove some results on the density and multiplicity of positive solutions to the conformal Q-
curvature equations P m (v)= K v n+ 2 mn− 2 m on the n-dimensional standard unit sphere …

We study the compactness properties of metrics of prescribed fractional Q‐curvature of order
3 in R 3. We will use an approach inspired from conformal geometry, seeing a metric on a …

In this paper, we study the local behavior of positive singular solutions to the equation (−∆)
σu= unn− 2σ in B1\{0} where (−∆) σ is the fractional Laplacian operator, 0< σ< 1 and nn− 2σ …

We study nonnegative solutions to the following Hardy-H\'enon type equations involving
higher order fractional Laplacians $$(-\Delta)^\sigma u=| x|^{-\alpha} u^{p} …

By developing a unified approach based on integral representations, we establish sharp
quantitative stability estimates for critical points of the fractional Sobolev inequalities induced …

In this paper, we are devoted to studying the positive weak, punctured or distributional
solutions to the biharmonic Lane-Emden equation\begin {equation*}\Delta^{2} u …

We mainly show that for a conformal metric $ g= u^{\frac {4}{n-2m}}| dx|^ 2$ on $\mathbb
{R}^ n $ with $ n\geq 2m+ 1$, if the higher order Q-curvature $ Q^{(2m)} _g $ is positive and …