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Construction of solutions for the critical polyharmonic equation with competing potentials
Wenjing Chen, Zexi Wang
In this paper, we consider the following critical polyharmonic equation \begin{align*}%\label{abs} ( -Δ)^m u+V(|y'|,y'')u=Q(|y'|,y'')u^{m^*-1},\quad u>0, \quad y=(y',y'')\in \mathb…
New type of solutions for the critical Lane-Emden system
Wenjing Chen, Xiaomeng Huang
In this paper, we consider the critical Lane-Emden system \begin{align*} \begin{cases} -Δu=K_1(y)v^p,\quad y\in \mathbb{R}^N,&\\ -Δv=K_2(y)u^q,\quad y\in \mathbb{R}^N,&\\ u,v>0, \e…
Blow-up solutions concentrated along minimal submanifolds for asymptotically critical Lane-Emden systems on Riemannian manifolds
Wenjing Chen, Zexi Wang
Let and be two Riemannian manifolds of dimensions and , respectively. Let , . The warped product $\mathcal{M}…
Multiple blowing-up solutions for asymptotically critical Lane-Emden systems on Riemannian manifolds
Wenjing Chen, Zexi Wang
Let be a smooth compact Riemannian manifold of dimension . We are concerned with the following elliptic system \begin{align*} \left\{ \begin{array}{ll} -…
Normalized solutions for a fractional -Laplacian Choquard equation with exponential critical nonlinearities
Wenjing Chen, Zexi Wang
In this paper, we are concerned with the following fractional -Laplacian Choquard equation \begin{align*} \begin{cases} (-Δ)^s_{N/s}u=λ|u|^{\frac{N}{s}-2}u +(I_μ*F(u))f(u),\ \…
Normalized ground states for a fractional Choquard system in
Wenjing Chen, Zexi Wang
In this paper, we study the following fractional Choquard system \begin{align*} \begin{split} \left\{ \begin{array}{ll} (-Δ)^{1/2}u=λ_1 u+(I_μ*F(u,v))F_u (u,v), \quad\mbox{in}\ \ \…