14 citations · 38 across the 49 of their papers we have counts for
9 papers · 2 filters
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…
Existence and concentration of multiple solutions for the fractional logarithmic Schrödinger-Poisson system via the penalization method
Jiao Luo, Zhipeng Yang
We study positive solutions of the fractional logarithmic Schrödinger-Poisson system \[ \begin{cases} \varepsilon^{2α}(-Δ)^αu+V(x)u+ϕu=u\log u^2+|u|^{q-2}u, & \text{in } \mathbb{R}…
On the existence of normalized solutions to a class of fractional Choquard equation with potentials
Yongpeng Chen, Zhipeng Yang, Jianjun Zhang
This paper investigates the existence of normalized solutions to the nonlinear fractional Choquard equation: $$ (-Δ)^s u+V(x) u=λu+f(x)\left(I_α*\left(f|u|^q\right)\right)|u|^{q-2}…
Bound states of nonlinear Dirac equations on periodic quantum graphs
Zhipeng Yang, Ling Zhu
We study nonlinear Dirac equations (NLDE) on periodic quantum graphs endowed with Kirchhoff-type vertex conditions. Our main goal is to establish existence and multiplicity of boun…
Critical fractional Kirchhoff problems: Uniqueness and Nondegeneracy
Zhipeng Yang, Yuanyang Yu
In this paper, we consider the following critical fractional Kirchhoff equation \begin{equation*} \Big(a+b{\int_{\mathbb{R}^{N}}}|(-Δ)^{\frac{s}{2}}u|^2dx\Big)(-Δ)^su=|u|^{2^*_s-2}…