1 citations · 3 across the 13 of their papers we have counts for
13 papers
Segregated Bubbling Solutions for a Critical Schrödinger System of Brezis--Nirenberg Type with Sublinear Competitive Coupling
Qing Guo, Chengxiang Zhang
We construct segregated bubbling solutions for a two-component critical Schrödinger system of Brezis--Nirenberg type in a smooth bounded domain , , wit…
Uniqueness of bound states for sublinear elliptic equations
Chengxiang Zhang, Xu Zhang
We investigate the uniqueness of radial bound state solutions to the sublinear elliptic equation \[ \begin{cases} -Δu - u + |u|^{q-2}u = 0 & \text{in } \mathbb{R}^n,\cr u(x) \to 0…
Multi-bump solutions for sublinear elliptic equations with nonsymmetric coefficients
Chengxiang Zhang, Xu Zhang
We investigate the existence of nonnegative bump solutions to the sublinear elliptic equation \[ \begin{cases} -Δv - K(x)v + |v|^{q-2}v = 0 & \text{in } \mathbb{R}^N, \\ v(x) \to 0…
Segregated solutions for nonlinear Schrödinger systems with sublinear coupling terms
Qing Guo, Chengxiang Zhang
We establish the existence of infinitely many nonnegative, segregated solutions for the sublinearly coupled Schrödinger system \begin{equation*} \left\{\begin{aligned}-Δu+K_1(x)u&=…
Segregated Solutions to Critical Elliptic Systems in High Dimensions ()
Zijuan Gao, Qing Guo, Chengxiang Zhang
We study the existence of multiple segregated solutions to the critical coupled Schrödinger system \[ \begin{cases} -Δu_{1} = K_1(| y|) | u_{1}|^{2^*-2}u_{1}+β| u_{2}|^{\frac{2^{*}…
Uniqueness and Nondegeneracy of ground states of $ -Δu + (-Δ)^s u+u = u^{p+1} \quad \hbox{in $\mathbb{R}^n$}$ when is close to and
Xifeng Su, Chengxiang Zhang, Jiwen Zhang
We are concerned with the mixed local/nonlocal Schrödinger equation \begin{equation} - Δu + (-Δ)^s u+u = u^{p+1} \quad \hbox{in ,} \end{equation} for arbitrary space…
A New Approach to Solving Singularly Perturbed NLS at Local Potential Maxima
Chengxiang Zhang
This paper presents a new approach for addressing the singularly perturbed nonlinear Schrödinger (NLS) equation: \begin{equation} -\varepsilon^2Δv + V(x) v =f(v),\ v>0,\ \lim_{|x|\…
Normalized clustering peak solutions for Schrödinger equations with general nonlinearities
Chengxiang Zhang, Xu Zhang
We are concerned with the normalized -peak solutions to the nonlinear Schrödinger equation \[ -\varepsilon^2Δv+V(x)v=f(v)+λv,\quad \int_{\mathbb{R}^N}v^2 =α\varepsilon^N. \]…
Qualitative analysis on logarithmic Schrödinger equation with general potential
Chengxiang Zhang, Luyu Zhang
In this paper, we study the existence, uniqueness, nondegeneracy and some qualitative properties of positive solutions for the logarithmic Schrödinger equations: \[ -Δu+ V(|x|) u=u…
Bound states for logarithmic Schrodinger equations with potentials unbounded below
Chengxiang Zhang, Xu Zhang
We study the existence and concentration behavior of the bound states for the following logarithmic Schrödinger equation \begin{equation*} \begin{cases} -\varepsilon^2Δv+V(x)v=v\lo…
Remarks on the Clark theorem
Guosheng Jiang, Kazunaga Tanaka, Chengxiang Zhang
The Clark theorem is important in critical point theory. For a class of even functionals it ensures the existence of infinitely many negative critical values converging to and…
Multi-bump solutions for logarithmic Schrödinger equations
Kazunaga Tanaka, Chengxiang Zhang
We study spatially periodic logarithmic Schrödinger equations: \begin{equation}\tag{LS} -Δu + V(x)u=Q(x)u\log u^2, \quad u>0\quad \text{in}\ \mathbb{R}^N, \end{equation} where $N\g…
The Brezis-Nirenberg problem for nonlocal systems
Luiz Faria, Olimpio Miyagaki, Fabio Pereira +2
By means of variational methods we investigate existence, non-existence as well as regularity of weak solutions for a system of nonlocal equations involving the fractional laplacia…