6 papers · 2 filters
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 -Laplacian operator $$ Δ_Φu \coloneqq \mbox{div} \left(ϕ(|\nabla u|)\dfrac{\nabla u}{|\nabl…
Existence of infinitely many solutions for a critical Hartree type equation with potential: local Pohožaev identities methods
Daniele Cassani, Minbo Yang, Xinyun Zhang
This paper deals with the following equation $$-Δu =K(|x'|, x'')\Big(|x|^{-α}\ast (K(|x'|, x'')|u|^{2^{\ast}_α})\Big) |u|^{2^{\ast}_α-2}u\quad\mbox{in}\ \mathbb{R}^N,$$ where $N\ge…