14 citations · 38 across the 49 of their papers we have counts for
35 papers · 1 filter
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…
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…
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…
Multiplicity of bound states for a class of nonlinear Dirac equations on generalized star graphs with potentials
Guangze Gu, Ziwei Li, Michael Ruzhansky +1
In this paper we investigate the existence and multiplicity of bound states for a class of nonlinear Dirac equations on a generalized star graph \(\mathcal{G}\): \[ -ic\,σ_1\,\part…
Nonrelativistic limit of bound-state solutions for nonlinear Dirac equation on noncompact quantum graphs
Guangze Gu, Michael Ruzhansky, Guoyan Wei +1
In this paper, we investigate the nonrelativistic limit and qualitative properties of bound-state solutions for the nonlinear Dirac equation (NLDE) defined on noncompact quantum gr…