Minbo Yang

Delaunay solutions to the fractional Hartree equation with critical growth

João Henrique Andrade, Tao Feng, Paolo Piccione +1

We study positive solutions of the critical fractional Hartree equation with a non-removable isolated singularity at the origin. This equation is doubly nonlocal, involving both th…

Blow-up asymptotics for a critical Hartree-type Brézis--Nirenberg problem in dimension three

Yue Wu, Minbo Yang

In this paper, we study the following critical Hartree problem \begin{equation}\label{equationabstract} \begin{cases} \displaystyle-Δu+(Q+\varepsilon V)u= A_{3,μ} \left(\int_Ω\frac…

Energy asymptotics and blow-up phenomena for biharmonic Brézis-Nirenberg problem

Jiamo Li, Qikai Lu, Minbo Yang

For dimensions $n \geq 8$ , we are concerned with the quotient functional of the biharmonic Brézis-Nirenberg problem under the Navier boundary condition $$ S(\varepsilon V):=\inf_{0\n…

Asymptotic behavior of solutions to a planar Hartree equation with isolated singularities

Tao Feng, Minbo Yang, Xianmei Zhou

In this paper we investigate the isolated singularities of the Hartree type equation \begin{equation*} -Δu (x)= \left(\frac{1}{|x|^α}*e^u\right)e^{u(x)}\quad \text{in } B_{1}\setmi…

Boundary regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals with non-standard growth

Pedro Fellype Pontes, João Vitor da Silva, Minbo Yang

For a fixed constant $λ > 0$ and a bounded Lipschitz domain $Ω \subset R^{n}$ with $n \geq 2$ , we establish that almost-minimizers (functions satisfying a sort of variational…

Qualitative properties of blowing-up solutions of nonlinear elliptic equations with critical Sobolev exponent

Minbo Yang, Shunneng Zhao

In this paper, we are concerned with the critical elliptic equation \begin{equation}\label{kx} \left\lbrace\begin{aligned} &-Δu=u^{p}+εκ(x)u^{q}\quad\hspace{2mm} \mbox{in}~~Ω, \\&u…

Compactness of Extremals for Singular Anisotropic Trudinger-Moser functionals on bounded domain

Weiwei Shan, Minbo Yang, Jiazheng Zhou

In this paper, we investigate the compactness of extremal functions for a critical singular anisotropic Trudinger-Moser inequality established by Lu-Shen-Xue-Zhu\cite{ref1}. We pro…

Qualitative properties of single blow-up solutions for nonlinear Hartree equation with slightly subcritical exponent

Alessandro Cannone, Silvia Cingolani, Minbo Yang +1

In this paper, we study the qualitative properties of single blow-up solutions to the nonlocal equations with slightly subcritical exponents \begin{equation*} -Δu=(|x|^{-(n-2)}\ast…

Asymptotic behavior of least energy solutions to the nonlinear Hartree equation near critical exponent

Silvia Cingolani, Minbo Yang, Shunneng Zhao

In this paper, we study that the nearly critical nonlocal problem \begin{equation*} \left\lbrace \begin{aligned} &-Δu=(|x|^{-{(n-2)}}\ast u^{p-ε})u^{p-1-ε} \quad \mbox{in}\quad Ω,…

Nondegeneracy of positive solutions for critical Hartree equation on Heisenberg group and it's applications

Minbo Yang, Shuijin Zhang

We study the uniqueness and nondegeneracy of positive bubble solutions for the generalized energy-critical Hartree equation on the Heisenberg group $H^{n}$ , \begin{equatio…

Lipschitz regularity of weakly coupled vectorial almost-minimizers for Alt-Caffarelli functionals in Orlicz spaces

Pedro Fellype Pontes, João Vitor da Silva, Minbo Yang

For a fixed constant $λ > 0$ and a bounded Lipschitz domain $Ω \subset R^{n}$ with $n \geq 2$ , we establish that almost-minimizers (functions satisfying a sort of variational…

Asymptotic behavior of solutions to critical Hartree equations with isolated singularities

João Henrique Andrade, Tao Feng, Paolo Piccione +1

We investigate the qualitative properties of positive classical solutions $u$ to critical Hartree equations on punctured domains, assuming that $u (x) \to + \infty$ as $x \to 0$ . For the…

Remainder terms, profile decomposition and sharp quantitative stability in the fractional nonlocal Sobolev-type inequality with $n > 2 s$

Qikai Lu, Minbo Yang, Shunneng Zhao

In this paper, we study the following fractional nonlocal Sobolev-type inequality \begin{equation*} C_{HLS}\bigg(\int_{\mathbb{R}^n}\big(|x|^{-μ} \ast |u|^{p_s}\big)|u|^{p_s} dx\bi…

Stability estimates for critical points of a nonlocal Sobolev-type inequality

Minbo Yang, Shunneng Zhao

In this paper, we study the stability of the following nonlocal Soblev-type inequality \begin{equation*} C_{HLS}\big(\int_{\mathbb{R}^n}\big(|x|^{-μ} \ast u^{p}\big)u^{p} dx\big)^{…

On elliptic equations with N-independent stable operators

Lele Du, Minbo Yang

We investigate the positive solutions of the semilinear elliptic equation \begin{align*} \sum^{N}_{i=1}\left(-\partial_{ii}\right)^{s}u=u^{p} \end{align*} with one-dimensional symm…

Infinitely many synchronized solutions for a nonlocal critical Hamiltonian elliptic system

Weiwei Ye, Minbo Yang

We establish the existence of infinitely many synchronized solutions for a class of critical Hamiltonian elliptic systems with Hartree-type nonlocal interactions.

Asymptotic behavior of solutions for a critical heat equation with nonlocal reaction

Jian Zhang, Jacques Giacomoni, Vicentiu Radulescu +1

In this paper, we consider the following nonlocal parabolic equation \begin{equation*} u_{t}-Δu=\left( \int_Ω\frac{|u(y,t)|^{2^{\ast}_μ}}{|x-y|^μ}dy\right) |u|^{2^{\ast}_μ-2}u,\ \t…

Single-peak and multi-peak solutions for Hamiltonian elliptic systems in dimension two

Hui Zhang, Minbo Yang, Jianjun Zhang +1

This paper is concerned with the Hamiltonian elliptic system in dimension two\begin{equation*}\aligned \left\{ \begin{array}{lll} -ε^2Δu+V(x)u=g(v)\ & \text{in}\quad \mathbb{R}^2,\…

A two-phase problem with degenerate operator in Orlicz-Sobolev spaces

Pedro F. Silva Pontes, Minbo Yang

In this paper we are interested in the study of a two-phase problem equipped with the $Φ$ -Laplacian operator $$ Δ_Φu \coloneqq \mbox{div} \left(ϕ(|\nabla u|)\dfrac{\nabla u}{|\nabl…