7 papers
Symmetry, monotonicity, and asymptotics of singular solutions to semilinear elliptic equations
Xusheng Du, Hui Yang
In this paper, we study singular positive solutions to the semilinear elliptic equation where is a bounded or u…
Asymptotic expansions for conformal scalar curvature equations near isolated singularities
Xusheng Du, Hui Yang
In this paper, we study asymptotic expansions of positive solutions of the conformal scalar curvature equation $$ - Δu = K(x) u^\frac{n + 2}{n - 2} ~~~~~~ \textmd{in} ~ B_1 \setmin…
Existence of solutions to a conformally invariant integral equation involving Poisson-type kernels
Xusheng Du, Tianling Jin, Hui Yang
In this paper, we study existence of solutions to a conformally invariant integral equation involving Poisson-type kernels. Such integral equation has a stronger non-local feature…
Blow up limits of the fractional Laplacian and their applications to the fractional Nirenberg problem
Xusheng Du, Tianling Jin, Jingang Xiong +1
We show a convergence result of the fractional Laplacian for sequences of nonnegative functions without uniform boundedness near infinity. As an application, we construct a sequenc…
A priori estimates versus arbitrarily large solutions for fractional semi-linear elliptic equations with critical Sobolev exponent
Xusheng Du, Hui Yang
We study positive solutions to the fractional semi-linear elliptic equation with an isolated singu…
Large singular solutions for conformal -curvature equations on
Xusheng Du, Hui Yang
In this paper, we study the existence of positive functions such that the conformal -curvature equation \begin{equation}\label{001} P_m (v) =K v^{\frac…
Local behavior of positive solutions of higher order conformally invariant equations with a singular set
Xusheng Du, Hui Yang
We study some properties of positive solutions to the higher order conformally invariant equation with a singular set $$ (-Δ)^m u = u^{\frac{n+2m}{n-2m}} ~~~~~~ \textmd{in} ~ Ω\bac…