In this paper, we aim to develop the (direct) method of scaling spheres, its integral forms,
and the method of scaling spheres in a local way. As applications, we investigate Liouville …

We mainly show the nondegeneracy of positive bubble solutions for generalized energy-
critical Hartree equations (NLH)\begin {equation*}-{\Delta u}\sts {x}-{\bm\alpha}\sts …

In this paper, we study the positive radial solutions for the Hénon equations with weighted
critical exponents on the unit ball BB in ℝ NR^ N with N⩾ 3 N\geqslant 3. We first confirm …

In this paper, we study the critical Hénon problem with non-power type perturbation. We use
the reduction argument to construct a family of bubbling solutions concentrating at the origin …

This paper deals with the following radial Caffarelli-Kohn-Nirenberg-type inequality,∫ RN| x|
α| Δ u| 2 dx≥ S rad (N, α)(∫ RN| x| l| u| p α⁎ dx) 2 p α⁎, u∈ C c∞(RN), where N≥ 3, 2< α< …

By using a suitable transform related to Sobolev inequality, we investigate the sharp
constants and optimizers in radial space for the following weighted Caffarelli-Kohn …

In this paper, we are concerned with the critical (ie, n-th) order Hénon-Lane-Emden type
equations with Navier boundary conditions on a half space R+ n:(0.1){(− Δ) n 2 u (x)= f (x, u …

This paper is devoted to radial solutions of the following weighted fourth-order equation div
(| x| α∇(div (| x| α∇ u)))=| u| 2 α∗∗− 2 u in RN, where N≥ 2, 4− N 2< α< 2 and 2 α∗∗= 2 …

In this paper we study the following eigenvalue problem {− Δ v= λ C (α)(p α− ε)| x| α u ε p α−
ε− 1 v in Ω, u= 0 on∂ Ω, where Ω⊂ RN is a smooth bounded domain containing the origin …

In this paper we study the problem where Ω= ℝ N or Ω= B 1, N⩾ 3, p> 1 and. Using a
suitable map we transform problem (1) into another one without the singularity 1/| x| 2. Then …