14 citations · 38 across the 49 of their papers we have counts for
52 papers
Sharp stability for mixed bubbles on hyperbolic space
Juncheng Wei, Zetian Yan, Zhipeng Yang
We prove sharp residual stability estimates for the critical Poincaré-Sobolev equation near sums of one positive hyperbolic solution and one projected Euclidean bubble in dimension…
Strict ground-level gaps on long-pendant generalized star graphs for nonlinear Dirac equations
Zhipeng Yang
We study strict ground-level gaps for autonomous nonlinear Dirac equations on noncompact metric graphs. The relevant level at infinity is the autonomous full-line level \(d_λ^\inft…
A Sharp Mass Threshold for Fractional Choquard Equations with Lower Hardy-Littlewood-Sobolev and \(L^2\)-Critical Terms
Yongpeng Chen, Zhipeng Yang
For \(\frac12\le s<1\), we study a fractional Choquard equation with prescribed mass and nonlinearities at the lower Hardy-Littlewood-Sobolev and \(L^2\)-critical exponents. The sh…
Sub-Laplacians on Compact Lie Groups: Heat Kernels, Distance, and Zeta Determinants
Wolfram Bauer, Zhicheng Han, Zhipeng Yang
We study heat kernels, sub-Riemannian distances, and spectral zeta functions of sub-Laplacians determined by closed connected subgroups of compact Lie groups. Combining Hall's inve…
Topological Effects on Bubbling in the Critical Dirichlet Problem on Hyperbolic Domains:
Tapendu Rana, Michael Ruzhansky, Zhipeng Yang
Let \(Ω\Subset\mathbb H^N\), \(N\in\{3,4,5\}\), be a bounded connected \(C^2\) domain. We prove that the pure critical Dirichlet problem \[ -Δ_{\mathbb H}u=u^{\frac{N+2}{N-2}} \qua…
Isolated Singularities for Fractional Hartree Equations
Guangze Gu, Aleks Jevnikar, Zhipeng Yang
We study isolated singularities of positive solutions to a fractional Hartree equation with Riesz interaction, \[ (-Δ)^s u = \left( \int_{\mathbb{R}^N\setminus\{0\}} \frac{u^p(y)}{…
Local well-posedness for nonlinear Dirac equation on -star metric graphs
Huichao Xing, Zhipeng Yang
We consider the Cauchy problem for the nonlinear Dirac equation on a noncompact -star metric graph , \[ \mathrm{i}\partial_t ψ= Dψ- |ψ|^{p-2}ψ, \qquad ψ(0)=ψ_0, \] where $p\g…
A positive ground state for a planar Choquard equation with mixed diffusion and critical exponential growth
Shaoxiong Chen, Sekhar Ghosh, Vishvesh Kumar +1
We study a two-dimensional Choquard equation driven by the mixed local and nonlocal operator , where the nonlinearity has critical exponential growth of Trudinger--Mo…
Infinitely many sign-changing solutions for logarithmic Schrödinger equations via an \(L^p\)-perturbation approach
Chen Huang, Zhipeng Yang, Jiazheng Zhou
We study the logarithmic Schrödinger equation \[ -Δu+V(x)u=u\log u^2,\qquad x\in\mathbb R^N,\ N\ge3. \] Since the logarithmic energy is not \(C^1\) on the natural space \(H_V^1(\ma…
Low-regularity well-posedness for a mixed-sign quadratic Dirac equation on -star metric graphs
Huichao Xing, Zhipeng Yang
We study the Cauchy problem for a mixed-sign quadratic Dirac equation on a noncompact -star metric graph , \[ \mathrm{i}\partial_t ψ= Dψ- \mathcal N(ψ), \qquad ψ(0)=ψ_0, \] w…
Higher-Order Heat Estimates and Semilinear Heat Equations on the Noncommutative Torus
Fulin Yang, Zhipeng Yang
We establish sharp higher-order heat estimates with complete bound on the noncommutative tori \(\mathbb{T}_θ^{n}\) and show the optimality in the small-time order. As an applicatio…
Fractional Sobolev-type embedding on CR sphere and Heisenberg group
Zongxiong Ren, Zhipeng Yang
This paper studies critical fractional Sobolev inequalities with lower-order terms on the standard CR sphere . Let , let , let , and let…
Normalized solutions for a class of fractional Choquard equations with the HLS lower critical term and a nonlocal perturbation
Shaoxiong Chen, Vishvesh Kumar, Zhipeng Yang +1
In this paper, we study the mass-constrained fractional Choquard equation \( (-Δ)^s u = λu + α(I_μ* |u|^{\frac{2N-μ}{N}})|u|^{\frac{2N-μ}{N}-2}u + (I_μ* |u|^p)|u|^{p-2}u \) in \( \…
Existence and Concentration of Multiple Positive Solutions for a Logarithmic Fractional Schrödinger--Poisson System
Jiao Luo, Zhipeng Yang
We study a logarithmic fractional Schrödinger--Poisson system in \(\R^{3}\): \begin{equation*} \begin{cases} \varepsilon^{2α}(-Δ)^αu+V(x)u+ϕu=u\log u^{2}+|u|^{p-2}u, & \text{in }\R…
Improved Sobolev Inequalities on the Quaternionic Sphere
Zongxiong Ren, Zhipeng Yang
In this paper we establish improved Sobolev inequalities on the quaternionic sphere under higher-order moment vanishing conditions with respect to the measure \(|u|^{p^*}\,dξ\). As…
Improved Fractional Sobolev Embeddings on Closed Riemannian Manifolds under Isometric Group Actions
Hao Tan, Zhipeng Yang
In this paper, we study symmetry-improved fractional Sobolev embeddings on closed Riemannian manifolds under the action of compact isometry groups. We prove that \(G\)-invariant fr…
Existence of positive and sign-changing solutions for a Choquard equation involving mixed local and nonlocal operators
Shaoxiong Chen, Hichem Hajaiej, Min Yang +1
We study the Choquard equation involving mixed local and nonlocal operators \[ -Δu + (-Δ)^{s}u + V(x)u = \left(\frac{1}{|x|^μ} * F(u)\right) f(u) \quad \text{in } \mathbb{R}^{2}, \…
Spectral properties and bound states of the Dirac equation on periodic quantum graphs
Zhipeng Yang, Ling Zhu
We investigate nonlinear Dirac equations on a periodic quantum graph and develop a variational approach to the existence and multiplicity of bound states. After introducing the…
Existence and concentration of ground state solutions for an exponentially critical Choquard equation involving mixed local-nonlocal operators
Shaoxiong Chen, Min Yang, Zhipeng Yang
We study the Choquard equation involving mixed local and nonlocal operators \[-\varepsilon^{2}Δu+\varepsilon^{2s}(-Δ)^{s}u+V(x)u=\varepsilon^{μ-2}\left(\frac{1}{|x|^μ}*F(u)\right)f…
On a class of logarithmic Schrödinger equations via perturbation method
Chen Huang, Zhipeng Yang
In this paper, we consider the following logarithmic Schrödinger equation \[ -Δu + V(x)u = u \log u^{2},\quad x\in\mathbb{R}^{N}. \] Assuming that \(V\in C(\mathbb{R}^{N},\mathbb R…
Sharp Fractional Sobolev Embeddings on Closed Manifolds
Hao Tan, Zetian Yan, Zhipeng Yang
We develop an intrinsic, heat-kernel based fractional Sobolev framework on closed Riemannian manifolds and study the critical fractional Sobolev embedding. We determine the optimal…
Convexification Numerical Method for Imaging of Moving Targets
Michael V. Klibanov, Jingzhi Li, Vladimir G. Romanov +1
The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and…
Normalized solutions for a class of fractional Choquard equations with mixed nonlinearities
Shaoxiong Chen, Zhipeng Yang, Xi Zhang
In this paper we study the following fractional Choquard equation with mixed nonlinearities: \[ \left\{ \begin{array}{l} (-Δ)^s u = λu + α\left( I_μ* |u|^q \right) |u|^{q-2} u + \l…
Normalized Solutions and Semiclassical Concentration for Upper-Critical Fractional Choquard Equations
Yergen Aikyn, Yongpeng Chen, Michael Ruzhansky +1
We study a fractional Choquard equation with an upper-critical Hartree term, an -supercritical Hartree perturbation, and a semiclassical potential under a prescribed -mas…