173 citations · 449 across the 41 of their papers we have counts for
9 papers · 1 filter
The Nehari manifold for fractional systems involving critical nonlinearities
Xiaoming He, Marco Squassina, Wenming Zou
We study the combined effect of concave and convex nonlinearities on the number of positive solutions for a fractional system involving critical Sobolev exponents. With the help of…
On critical -Laplacian systems
Zhenyu Guo, Kanishka Perera, Wenming Zou
We consider the critical -Laplacian system \begin{equation}\label{92} \begin{cases}-Δ_p u-\frac{λa}{p}|u|^{a-2}u|v|^b =μ_1|u|^{p^\ast-2}u+\frac{αγ}{p^\ast}|u|^{α-2}u|v|^β, &x\in…
On a doubly critical Schrödinger system in $\bbr^4$ with steep potential wells
Yuanze Wu, Wenming Zou
Study the following two-component elliptic system% \begin{equation*} \left\{\aligned&Δu-(λa(x)+a_0)u+u^3+βv^2u=0\quad&\text{in }\bbr^4,\\% &Δv-(λb(x)+b_0)v+v^3+βu^2v=0\quad&\text{i…
Existence of extremal functions for a family of Caffarelli-Kohn-Nirenberg inequalities
Xuexiu Zhong, Wenming Zou
Consider the following inequalities due to Caffarelli, Kohn and Nirenberg {\it (Compositio Mathematica,1984):} $$\Big(\int_Ω\frac{|u|^r}{|x|^s}dx\Big)^{\frac{1}{r}}\leq C(p,q,r,μ,σ…
On Elliptic Systems involving critical Hardy-Sobolev exponents (Part II)
Xuexiu Zhong, Wenming Zou
This paper is the second part of a work devoted to the study of elliptic systems involving multiple Hardy-Sobolev critical exponents: $$\begin{cases} -Δu-λ\frac{|u|^{2^*(s_1)-2}u}{…
A nonlinear elliptic PDE with multiple Hardy-Sobolev critical exponents in
Xuexiu Zhong, Wenming Zou
In this paper, we will study the following PDE in involving multiple Hardy-Sobolev critical exponents: $$ \begin{cases} Δu+\sum_{i=1}^{l}λ_i \frac{u^{2^*(s_i)-1}}{|x…