7 papers · 1 filter
Uniqueness and Nondegeneracy of Ground State for the -Critical Boson Star Equation
Pan Chen, Qi Guo, Juncheng Wei +1
We prove uniqueness, up to phase rotations and translations, of the ground state for the -critical boson star equation \[ (\sqrt{-Δ}+1)Q =\bigl(|x|^{-1}* |Q|^2\bigr)Q, \qquad…
Uniqueness, Nondegeneracy, and Asymptotic Expansions of Ground States for the Dirac-Coulomb System
Pan Chen, Qi Guo, Xiaoyu Zeng
We study ground states of the following Dirac-Coulomb system $$\mathscr{D}_cu_c- \left(\abs{x}^{-1}\ast \abs{u_c}^2\right)u_c=ω_cu_c,$$ under the constraint $\norm[L^2]{u_c}^2=1.$F…
Multiplicity and Nonrelativistic limit of Bound States of Nonlinear Dirac Equations on Noncompact Metric Graphs with Localized Nonlinearities
Pan Chen, Qi Guo
In this paper, we investigate the multiplicity of normalized solutions to a nonlinear Dirac equation with localized nonlinearities on noncompact metric graphs under the \(L^2\)-con…
Energy quantization for Dirac systems over non-collapsed degenerating Einstein manifolds
Pan Chen, Youmin Chen, Miaomiao Zhu
We study energy quantization for a class of Dirac systems on compact spin Einstein manifolds of dimension \(n\). For a sequence of solutions to a nonlinear Dirac system with unifor…
Existence and nonrelativistic limit of ground states to nonlinear Dirac equation
Pan Chen, Yanheng Ding, Qi Guo
This paper explores the existence and properties of ground states, including both energy and action ground states, for nonlinear Dirac equations with power-type potentials. \begin{…
Asymptotic properties of non-relativistic limit for pseudo-relativistic Hartree equations
Pan Chen, Vittorio Coti Zelati, Yuanhong Wei
In this paper, we study the asymptotic behavior of energy and action ground states to the following pseudo-relativistic Hartree equation \[ \left(\sqrt{-c^2Δ+m^2c^4}-mc^2\right)u +…
Nonrelativistic Limit of Normalized Solutions to a class of nonlinear Dirac equations
Pan Chen, Yanheng Ding, Qi Guo +1
In this paper, we investigate the nonrelativistic limit of normalized solutions to a nonlinear Dirac equation as given below: \begin{equation*} \begin{cases} &-i c\sum\limits_{k=1}…