20 citations · 41 across the 19 of their papers we have counts for
20 papers
Improved Lerey inequality and Trudinger-Moser type inequality involving the Leray potential
Huyuan Chen, Yihong Du, Feng Zhou
We obtain three types of results in this paper. Firstly we improve Leray's inequality by providing several types of reminder terms, secondly we introduce several Hilbert spaces bas…
On semilinear elliptic equation with negative exponent arising from a closed MEMS model
Huyuan Chen, Ying Wang, Feng Zhou
This paper is concerned with the elliptic equation in a connected, bounded domain of subject to zero Dirichlet boundary conditions,…
Isolated singularities for fractional Lane-Emden equations in the Serrin's supercritical case
Huyuan Chen, Feng Zhou
In this paper, we give a classification of the isolated singularities of positive solutions to the semilinear fractional elliptic equations $$(E) \quad\quad (-Δ)^s u = |x|^θ u^{p}\…
Nonlinear Potential Estimates for Generalized Stokes System
Lingwei Ma, Zhenqiu Zhang, Feng Zhou
In this paper, we consider the generalized stationary Stokes system with -growth and Dini- regular coefficients. The main purpose is to establish pointwise e…
On isolated singular solutions of semilinear Helmholtz equation
Huyuan Chen, Feng Zhou
Our purpose of this paper is to study isolated singular solutions of semilinear Helmholtz equation $$ -Δu-u=Q|u|^{p-1}u \quad{\rm in}\ \ \mathbb{R}^N\setminus\{0\},\ \qquad\lim_{|x…
Bounds of Dirichlet eigenvalues for Hardy-Leray operator
Huyuan Chen, Feng Zhou
The purpose of this paper is to study the eigenvalues for the Dirichlet Hardy-Leray operator, i.e. $$ -Δu+μ|x|^{-2}u=λu\ \ {\rm in}\ \, Ω,\quad\quad u=0\ \ {\rm on…
Qualitative properties of Hénon type equations with exponential nonlinearity
Zongming Guo, Xia Huang, Dong Ye +1
We are interested in the qualitative properties of solutions of the Hénon type equations with exponential nonlinearity. First, we classify the stable at infinity solutions of $Δu +…
Solutions of nonhomogeneous equations involving Hardy potentials with singularities on the boundary
Huyuan Chen, Axander Quaas, Feng Zhou
In this paper, we present a new distributional identity for the solutions of elliptic equations involving Hardy potentials with singularities located on the boundary of the domain.…
Singular Behavior of an Electrostatic--Elastic Membrane System with an External Pressure
Yujin Guo, Yanyan Zhang, Feng Zhou
We analyze nonnegative solutions of the nonlinear elliptic problem , where and , on a bounded domain of () with a…
On Gaussian curvature equations in with prescribed non-positive curvature
Huyuan Chen, Feng Zhou, Dong Ye
The purpose of this paper is to study the solutions of with . We introduce the following quantity: $$α_p(K)=\sup\left…
Asymptotic behaviors of governing equation of Gauged Sigma model for Heisenberg ferromagnet
Huyuan Chen, Feng Zhou
In this note, we study weak solutions of equation \begin{equation}\label{eq 00.1} Δu =\frac{4e^u}{1+e^u} -4π\sum^{N}_{i=1}δ_{p_i}+4π\sum^{M}_{j=1}δ_{q_j} \quad{\rm in}\;\; \mathbb{…
Radial symmetry of positive entire solutions of a fourth order elliptic equation with a singular nonlinearity
Zongming Guo, Long Wei, Feng Zhou
The necessary and sufficient conditions for a regular positive entire solution of the biharmonic equation: \begin{equation} \label{0.1} -Δ^2 u=u^{-p} \;\; \mbox{in $\R^N \; (N…
Nonexistence of Positive Supersolution to a Class of Semilinear Elliptic Equations and Systems in an Exterior Domain
Huyuan Chen, Rui Peng, Feng Zhou
In this paper, we primarily consider the following semilinear elliptic equation \begin{eqnarray*} \arraycolsep=1pt\left\{ \begin{array}{lll} \displaystyle -Δu= h(x,u)\quad \ &{\rm…
Fast decaying solutions of Lane-Emden equations involving nonhomogeneous potential
Huyuan Chen, Xia Huang, Feng Zhou
We are interested in studying positive solutions of Lane-Emden equation where is a nonhomogeneous potential sati…
Isolated singularities for elliptic equations with Hardy operator and source nonlinearity
Huyuan Chen, Feng Zhou
In this paper, we concern the isolated singular solutions for semi-linear elliptic equations involving the Hardy-Leray potentials \begin{equation}\label{0} -Δu+\fracμ{|x|^2} u=u^p\…
On nonhomogeneous elliptic equations with the Hardy-Leray potentials
Huyuan Chen, Alexander Quaas, Feng Zhou
In this paper, we present some suitable distributional identities of the solutions for nonhomogeneous elliptic equations involving the Hardy-Leray potentials and study qualitative…
Isolated singularities of positive solutions for Choquard equations in sublinear case
Huyuan Chen, Feng Zhou
Our purpose of this paper is to study the isolated singularities of positive solutions to Choquard equation in the sublinear case $$\displaystyle \ \ -Δu+ u =I_α[u^p]…
On semi-linear elliptic equation arising from Micro-Electromechanical Systems with contacting elastic membrane
Huyuan Chen, Ying Wang, Feng Zhou
This paper is concerned with the nonlinear elliptic problem on a bounded domain of with Dirichlet boundary conditions. This problem arise…
Classification of isolated singularities of positive solutions for Choquard equations
Huyuan Chen, Feng Zhou
In this paper we classify the isolated singularities of positive solutions to Choquard equation and prove the existence of isolated singular solutions.
Regularity of the extremal solution for some elliptic problems with advection
Xue Luo, Dong Ye, Feng Zhou
In this note, we investigate the regularity of extremal solution for semilinear elliptic equation on a bounded smooth domain of $\mathb…